‘4 I ‘.‘...y.- 1-H - G ‘ <‘ ' ‘ “ ' ‘ . T .. . T....4-T v‘yw W' Tn. ‘ .. . .. ' ' DYNAMIC PROPERTIES OF ICE AND FROZEN CLAY UNDER CYCLIC TRIAXIAL LOADING CONDITIONS ._ W . .7 '7 A A 7 Dissertation for the Degree of Ph D 7 _ . »_ MICHIGAN STATE UNIvERsITY , ¥ THIRA CHAICHANAVONG _ _ ' ’- .11976* :*\:’.=‘< L TB? 5 RY Michigan gate University- This is to certify that the thesis entitled DYNAMIC PROPERTIES OF ICE AND FROZEN CLAY UNDER CYCLIC TRIAXIAL LOADING CONDITIONS presented by Thira Chaichanavong has been accepted towards fulfillment of the requirements for Ph. D. degree in Civil Engineering MSVW Major professor Date February 17, 1976 0-7639 ABSTRACT DYNAMIC PROPERTIES OF ICE AND FROZEN CLAY UNDER CYCLIC TRIAXIAL LOADING CONDITIONS BY Thira Chaichanavong In the past decade it has been demonstrated that a significant relationship exists between the response of a structure during an earthquake and the dynamic char— acteristics of the soil deposit on which it is founded. Research in this area has progressed to the point where analytic techniques are now available for predicting this response interaction between a soil deposit and a struc— ture during an earthquake. To compute the response interaction two soil properties are required: (1) the dynamic shear modulus (related to dynamic Young's modu— lus), and (2) the damping ratio. For unfrozen soils these properties have been determined by several inves— tigators and design equations and curves to establish the properties for representative soil types have been devel— Oped. For frozen soils, only limited work has been done to evaluate these properties in a test range that appar— mmiy would not be useful in earthquake response analyses, Thira Chaichanavong Thus, an engineer confronted with a seismic design prob— lem involving frozen soils cannot use existing analytic techniques to predict response interactions because the necessary properties of frozen soils have not been determined. As part of a long—term study to evaluate dynamic properties of frozen soils under simulated earthquake loading conditions, cyclic triaxial tests were performed on laboratory prepared samples of ice and frozen clay. The cyclic triaxial test setup consists of four basic components: (1) an MTS electrohydraulic closed loop test system which applies a cyclic deviator stress to the sample, (2) a triaxial cell which contains thesanple and noncirculating coolant, (3) a refrigeration unit and cold bath which circulates the coolant around the triaxial cell, (4) output recording devices to monitor the load (stress) and displacement (strain) of the sample during the test. The cylindrical polycrystalline ice samples used in the research program were prepared using natural snow and distilled water for high density samples (about 0.904 g/cc) or natural snow and carbonated water for low density samples (about 0.77 g/cc). The samples were 3 2 tested at strain amplitudes from 3 x 10- to 2 x 10. % temperatures from —1 to -lO°C, frequencies from 0.05 to 5 cps and confining pressures from O to 200 psi. The Thira Chaichanavong values of dynamic Young's modulus over the range of material and test conditions were from 260 x 103 to 900 x 103 psi; the values of damping ratio were from 0.001 to 0.14. The test results indicate that the dynamic Young's modulus of ice increases, in general, with increasing confining pressure, density, and fre— quency. The dynamic Young's modulus of ice decreases with increasing temperature and increasing strain ampli- tude. The test results indicate that, in general, damp- ing ratio of ice decreases as frequency increases from 0.05 to 1.0 cps and increases as frequency increases from 1.0 to 5.0 cps. The damping ratio tends to decrease with decreasing temperature and increases with increasing strain amplitude for high density ice. It is apparently not affected by strain amplitude for low density ice. There appears to be no well—defined relationship between damping ratio of ice and confining pressure or density. Two types of frozen clay samples were used in the research program: (1) Ontonagon clay, termed "O-clay," and (2) a mixture of Ontonagon and sodium montmorillon- ite clay (fifty percent each by weight), termed "M+O— clay." The O—clay was prepared at different water contents to assess the influence of water (ice) content midynamic properties. The M+O-clay was used to investi— gate the influence of specific surface area (related to unfrozen water content). The samples were tested at Thira Chaichanavong 3 1. strain amplitudes from 3 x 10— to l x 10— s, tempera— tures from —1 to -10°C, frequencies from 0.05 to 5 cps, and confining pressures from 0 to 200 psi. The values of dynamic Young's modulus over the range of test con— ditions were from 90 x 103 to 880 x 103 psi; the values of damping ratio were from 0.02 to 0.3. The test results indicate that the dynamic Young's modulus of frozen clay decreases with increasing strain amplitude and specific surface area. The dynamic Young‘s modulus of frozen clay increases with decreasing temperature and increasing water content and frequency. It is apparently not affected by confining pressure. The test results indi- cate that the damping ratio of frozen clay increases with increasing strain amplitude and increasing temperature. The damping ratio, in general, decreases for an increase in frequency from 0.05 to 5 cps; for frequencies greater than 5 cps, damping ratio increases as frequency increases. There appears to be no well-defined rela- tionship between the damping ratio and water content or specific surface area. The damping ratio is apparently not affected by confining pressure. The dynamic properties of ice and frozen clay obtained in the present study at the lowest strain ampli— tude were compared to those obtained in previous studies. The P-wave velocity of ice from the present study (calcu— lated from the dynamic Young's modulus) is approximately Thira Chaichanavong 38 percent lower than found in previous laboratory studies and 64 percent lower than found in previous field studies. It appears these differences can be explained by differences in the test techniques employed. The damping ratio of ice from the present study is close to the values obtained in previous studies. The P-wave velocity of frozen clay from the present study is nearly identical with the results from a previous study for a comparable type of clay. The damping ratio is higher than that reported in a previous study. DYNAMIC PROPERTIES OF ICE AND FROZEN CLAY UNDER CYCLIC TRIAXIAL LOADING CONDITIONS By Thira Chaichanavong A DISSERTATION Submitted to Michigan State University a1 fulfillment of the requirements for the degree of in parti DOCTOR OF PHILOSOPHY Department of Civil and Sanitary Engineering 1976 ACKNOWLEDGMENTS The writer wishes to express his sincere appreci- ation to his major academic advisor, Dr. Ted S. Vinson, for his encouragement, patience, and aid throughout the writer's doctoral studies and for his guidance during the preparation of this thesis. Thanks are also due the other members of the writer's guidance committee: Dr. 0. B. Andersland, Dr. R. K. Wen, and Dr. R. Carmichael. Appreciation is extended to Sheila Eddington and Gerry Wright for their help in the reduction of the experi— mental data. The writer wishes to thank the Royal Thai Govern- ment, the National Science Foundation (Grant ENG 74—13506) and the Division of Engineering Research at Michigan State University for their financial assistance. The writer also wants to pay special tribute to his wife, Pajanipan, and his daughter, Pook, for their Wonderful patience in waiting during the course of the writer's doctoral studies. ii LIST OF LIST OF LIST OF LIST OF Chapter I. II. TABLE OF CONTENTS TABLES . . . . . . . . . . . . FIGURES . . . . . . . . . APPENDICES . . . . . . . . . . . SYMBOLS . . . . . . . . . . . INTRODUCTION . . . . . . . 1.1 Statement of the Problem . . . . 1.2 Purpose and Scope of studies . . . 1.3 Mechanical Properties of Frozen Soils and Thermal Characteristics of Frozen Soil Deposits . . . . . 1.4 Dynamic Properties of Unfrozen Soils . . . . . . . '. . . . 1.5 Fundamentals of Cyclic Triax1a1 Testing . . . . . . . . . . DYNAMIC PROPERTIES OF ICE AND FROZEN LAY . . . C ' o I o o o o o o o 2.1 General . . . . . . . . °. . 2.2 Previous Methods to Evaluate Dynamic Properties of Ice and Frozen Clay 2.3 Dynamic Elastic Properties of Ice 2.3.1 Effect of Temperature . . . 2.3.2 Effect of Density . . . . 2.3.3 Effect of Frequency . . . 2.3.4 Effect of Confining Pressure 2.4 Damping of Ice . . . . . . . . 2.5 Dynamic Elastic Properties of Frozen Clay . . . . . . . . - 2.5.1 Effect of Void Ratio . . - 2.5.2 Effect of Ice Saturation . . 2.5.3 Effect of Temperature . . . 2.5.4 Effect of Frequency . . . . iii Page vi xxii xxiii AH ll 16 22 Chapter III. IV. 2.5.5 Effect of Unfrozen Water Content . . . 2.5.6 Effect of Dynamic Stress (or Strain) . . .6 Damping of Frozen Clay . . . . 7 Poisson's Ratio of Ice and Frozen Clay . . . . . . . . . . 2.7.1 Poisson's Ratio of Ice . . 2.7.2 Poisson's Ratio of Frozen Clay . . . . . . . NM SAMPLE PREPARATION, SAMPLE INSTALLATION, AXIAL CELL ASSEMBLY, AND TEST PROCEDURE General . . . . . . . . . Preparation of Ice Sample . . . Preparation of Frozen Clay Sample Sample Installation and Triaxial Cell Assembly . . . . . . . 3.5 Test Procedure . . . . . . . cutout» lwal-J DYNAMIC PROPERTIES OF ICE UNDER CYCLIC TRIAXIAL LOADING CONDITIONS . . . . 1 General . . . . . . . . 2 Test History Effects on Dynamic Properties . . . . . . . 4.3 Influence of Number of Cycles on Evaluation of Dynamic Properties 4.4 Dynamic Young's Modulus of Ice . 4.4.1 Effect of Strain Amplitude 4.4.2 Effect of Confining Pressure .3 Effect of Frequency . of Temperature .5 Effect of Density . . . ing Ratio of Ice . . . . . Effect of Strain Amplitude Effect of Frequency . . . of Temperature . . Effect of Density . . . Effect of Confining Pressur 4. 4. ¢»A.h 51> m H: [—h (D 0 fi- 0 o g n bd>¢sbJ>Uib¢>b C U1m ml CP, cp LIST OF SYMBOLS area of hysteresis loop area of triangle pore pressure parameter confining pressure Young's modulus Young's modulus (flexural vibration) Young's modulus (longitudinal vibration) complex Young's modulus frequency shear modulus complex shear modulus a factor relating relative density and strain amplitude specific surface area undrained Shear strength temperature loss factor compression wave velocity shear wave velocity unfrozen water content lag angle between stress vector and strain vector xxiii ax: lat ten dan Poi com den: axle axia mean 0' O G d comp d . exten51on I m axial strain lateral strain temperature damping ratio Poisson's ratio complex Poisson's ratio density axial stress in compression axial stress in tension mean principal effective stress xxiv 1: It is ge resources of Ala inmany cases re] resources in the line represents 1 reserves beneath Prejects will £01 with the can development 1 lIEtworks, and gent Occur. These wil' e“Dieters. As sh Dasha lies withi ofPerennially or DSign engineers Davior of frozen different from tha Further, A ”St active seismi ”54 "Good Friday" CHAPTER I INTRODUCTION 1.1 Statement of the Problem It is generally recognized that the natural resources of Alaska will be required to supplement, and in many cases replace, the dwindling reserves of natural resources in the conterminous states. The Alaska pipe— line represents the first major effort to tap the oil reserves beneath the North Slope; undoubtedly many other projects will follow. With the demand for natural resources, signifi- cant development of transportation systems, utility networks, and general civil and industrial works must occur. These will pose special design problems for engineers. As shown in Figure 1.1, nearly 85 percent of Alaska lies within a permafrost region, i.e., a region 0f Perennially or permanently frozen ground. Clearly, design engineers must have knowledge of the mechanical behavior of frozen soils, which can be significantly different from that of unfrozen soils. Further, Alaska is located in one of the world's “Est aCtive seismic zones. This was exemplified by the 1964 "Good Friday" earthquake and more than sixty other I!" I 0 W H'.‘ LLJ. 1 ... _. ll Iluolnluoul "In" ! u lulmnsr '2'" “‘5‘“ ~wc- “will” u... pnurnos CLIIATE mm... ""10me —. um Aunu Figure 1.] REGIO Brown L I22 0 la+ n IZ—ISA ‘5.5'C o 000...... \ Figure T. 76 ' . 7°C 2' ”malnflw ' 5 I l— \ _ ~o 3°c7"\.. 0., " 64- “\J‘ 107, —0 WI “5+ IBt'... I22 .ISQ , 25-49 4 r -53 ‘ v - » e“ PERIAFROST, mu m urrrns THICKNESS. DEPTH ro BASE NINIMUM THICKNESS, BASE UNKNOWN RELIC PERMAFROST. GROUND FROZEN BETWEEN DEPTHS SHOWN TEMPERATURE OF PERMAFROST AT [5 T0 25 METERS DEPTH PERMAFROST ZONE BOUNDARY CLIIATE APPROXIMATE POSITI MEAN ANNUAL AIR TEMPERATURE. 'C 1 REGIONAL ZONATION 0F PERMAFROST IN ALASKA (after Brown and Pewe, 1973) ON 0F MEAN ANNUAL AIR TEMPERATURE ISOTHERM, O'C earthquakes tha Iagnitude of 7 and Echols, 196 In the ] asignificant r1 of a structure r acteristics of 1 (Seed and Idrise has progressed t are nw availabl between a soil (3 quake. Engineer Alaska should be be able to apply To estab.‘ soil deposit and Wired: (1) t1 manic Young's (Idriss and Seed rEquirecl to dete iECted to vibrat Matias have "14 design equati D88 for represen [Hardin and Drnev frMen soils , onl earthquakes that have equaled or exceeded a Richter magnitude of 7 since the beginning of the 18005 (Davis and Echols, 1962). In the past decade it has been demonstrated that a significant relationship exists between the response of a structure during an earthquake and the dynamic char- acteristics of the soil deposit on which it is founded (Seed and Idriss, 1969 and 1971). Research in this area has prOgressed to the point where analytic techniques are now available for predicting the response interaction between a soil deposit and a structure during an earth- quake. Engineers concerned with future development in Alaska should be cognizant of these techniques and should be able to apply them in design practice. To establish the response interaction between a soil deposit and a structure, two soil properties are required: (1) the dynamic shear modulus (related to dynamic Young's modulus), and (2) the damping ratio (Idriss and Seed, 1968). (These properties are also required to determine the response of foundations sub— jected to vibratory loads.) For unfrozen soils these properties have been determined by several investigators, and design equations and curves to establish the proper— ties for representative soil types have been developed (Hardin and Drnevich, 1972; Seed and Idriss, 1970). FQr frozen soils, only limited work has been done to evaluate these propertie not be useful 1' an engineer cc involving froze techniques to p necessary prope determined . _l__._2_ The pur; (1) Eva] froz be u (2) Inve shea; modu.‘ froze The scop includes a detai teSt system and eValuate dynamic discussion of th A the experiment Dtained by previ "‘8 research work “Clinical proper these properties in a test range that apparently would not be useful in earthquake response analyses. Thus, an engineer confronted with a seismic design problem involving frozen soils cannot use existing analytic techniques to predict response interactions because the necessary properties of frozen soils have not been determined. 1.2 Purpose and Scope of Studies The purpose of this research program is to: (1 v Evaluate dynamic properties of ice and frozen clay under test conditions that would be useful for earthquake response analyses. (2) Investigate parameters that might influence shear moduli (related to dynamic Young's modulus) and damping ratios of ice and frozen clay. The scope of studies presented in this thesis includes a detailed description of the cyclic triaxial test system and experimental techniques employed to evaluate dynamic properties of ice and frozen clay, a discussion of the experimental results, and a comparison 0f the experimental results of the present study to those obtained by previous investigators. An understanding of the research work is enhanced by a knowledge of the mechanical properties of frozen soils and thermal characteristics properties of u triaxial testin sections of thi review of previ of ice and from tion given in C] laborame expel different from 1 gram. Chapter 1 Preparation of 5 tion of the samp used to test the description of t intern.) Chapte on the dynamic p: dYflalnic propertir tEITllxirature, con DAB. and number (bapter V the e ties of frozen 0 dmanic properti aPacific surface Wining pressu “Miler of cycles Wants a compar characteristics of frozen soil deposits, the dynamic properties of unfrozen soils, and fundamentals of cyclic triaxial testing. This is presented in the next three sections of this chapter. In Chapter II a thorough review of previous studies to evaluate dynamic properties of ice and frozen clay is presented. All of the informa— tion given in Chapter II is associated with field or laboratory experimental methods which are significantly different from the method employed in the research pro— gram. Chapter III provides information on the laboratory preparation of samples of ice and frozen clay, installa— tion of the samples in a triaxial cell, and the procedure used to test the samples. (Appendix A gives a detailed description of the components of the cyclic triaxial test system.) Chapter IV presents the experimental results on the dynamic properties of ice. The influence on dynamic properties caused by variations in density, temperature, confining pressure, frequency, strain ampli- tude, and number of cycles of loading is included. In Chapter V the experimental results on the dynamic proper— ties of frozen clay are presented. The influence on dynamic properties caused by variations in water content, Specific surface area of the clay mineral, temperature, confining pressure, frequency, strain amplitude, and number of cycles of loading is included. Chapter VI presents a comparison of the dynamic properties of ice summarizes the seuts conclusio Frozen Iineral particl water, and entr relative propor the mechanical b decade significa effects of these tWe. sustained Pressures. The : the following pa: It has be Hterials decrea: indegree of ice “at of the voluo ”11 mass. This “Entitled compre pmSsures up to 4 and frozen clay obtained in the research program to those obtained by previous investigators and a comparison of the dynamic properties of ice to those of frozen clay. A discussion of both comparisons is given. Chapter VII summarizes the results of the research program and pre— sents conclusions that can be reached. 1.3 Mechanical Properties of Frozen Soils and Thermal Characteristics of Frozen Soil Deposits Frozen soils are a multiphase system of soil mineral particles, polycrystalline ice, unfrozen pore water, and entrapped air. It would be expected that the relative proportions of these components would influence the mechanical behavior of frozen soils. In the past decade significant work has been done to determine the effects of these variables and the effects of tempera— ture, sustained loads, deformation rates, and confining pressures. The results of this work are summarized in the following paragraphs. It has been shown that the strength of sand-ice materials decreases approximately linearly with a decrease in degree of ice saturation, which is defined as the per- cent of the volume of ice to the volume of the voids in a soil mass. This conclusion has been reached for both unconfined compression tests and for tests with confining pressures up to 4800 kN/m2 (Alkire and Andersland, 1973; Goughnour and observed that the confining indication tha less dependent frictional in n The unf of ice saturati perature is a f (Dillon and And is shown in Fig unfrozen water increases. Beca nearly all avail tures slightly b Clays with high even at temperat Because the spec: a1w of 10-20 m‘ '2/9 for montmor: coIltents and, her c(’usitierable. Tl ai’i’reciably with Increasin the strength of f Wire, 1972 ; Ka Goughnour and Andersland, 1968). In general it has been observed that the reduction in strength decreases as the confining pressure increases. This is perhaps an indication that strength at high confining pressures is less dependent on the ice matrix and becomes primarily frictional in nature. The unfrozen water content (related to the degree of ice saturation) in soils at a given subfreezing tem- perature is a function of the specific surface area (Dillon and Andersland, 1966; Anderson and Tice, 1972). As shown in Figure 1.2, at a given temperature the unfrozen water content increases as the specific surface increases. Because of their low specific surface area, nearly all available water in sands is frozen at tempera— tures slightly below freezing (Scott, 1969). For clays with high specific areas, unfrozen water can exist even at temperatures below-30°C (Tsytovich, 1960). Because the specific surface area of clays varies from a low of 10—20 mZ/g for kaolinite to greater than 800 mz/g for montmorillonite, the range of unfrozen water contents and, hence, the mechanical properties can be considerable. The unfrozen water content does not change appreciably with temperature for temperatures below -lO°C. Increasing the strain rate will generally increase the strength of frozen soils in unconfined compression (Alkire, 1972; Kaplar, 1971), but the increase is only of no U n 0 Li a O 0 H o 5' I. 3 a 0 II o k ‘s‘ Figure 1.2 CALC VALU and *IOC ~20( Depth, -50C Meters -500 -600 Figure 1.3 ' (.00 I ‘5 0.00 (D u r: O U H 3 060 n W B u Nab/q C“ 3 0.40 o H E 0.20 Figure 1.2 Depth, Meters -2 . 9, Temperature C CALCULATED PHASE COMPOSITION CURVES FOR VARIOUS VALUES 0F SPECIFIC SURFACE AREA (after Anderson and Tice, 1972) Temperature, °C ‘ f r r 7* —é{\—4x -2\i 2 4 6 8 \ \ \ x \ \ \ ‘\ -lOO \\ \\ \\ \\ \ \ \ \ \ \\ \ \ . . \ \ \\ Average vanaflon \ \ x .200 \\ \ (after Terzaghi, l952) \ \\ \ \ \\ ‘300 \ \ \ \ \ ~4oo \\ \ Recorded temperatures \ in borehole -5oo \ \ \ \ \ ~eoo ‘ 0° hotherm Figure I. 3 TEMPERATURE VARIATION WITH DEPTH IN PERMAFROST (modified after Judge, 1973) the order of 1 order of magni from samples 1: indicate that a peak strength 91 percent for an (Mire, 1972) . The ult of frozen soils ing (freezing) increase can be lehperature. I iboutone-half o of these basic 5: strengths. It has be that frozen soil mom, 1970; An hiersland, 1968) Wider a constant its given time a diviator stress) ‘ t“Dentures. Th1 “leis will also : Finally, 1' Nine“ relations the order of 15 percent of the peak strength for an order of magnitude increase in the strain rate. Results from samples tested at 4800 kN/m2 confining pressure indicate that again there might be a slight increase in peak strength with strain rate, but it is at most 10 percent for an order of magnitude increase in the rate (Alkire, 1972). The ultimate compressive strength of all types of frozen soils has been found to increase with decreas— ing (freezing) temperature (Jumikus, 1966). This increase can be 300 percent or more for a 20°C change in temperature. In general, the strength of frozen clay is about one—half of the strength of frozen sand. Mixtures of these basic soil types will have intermediate strengths. It has been demonstrated by several investigators that frozen soil will exhibit creep (Andersland and AlNouri, 1970; Andersland and Akili, 1967; Goughnour and Andersland, 1968), i.e., an increase in strain with time under a constant applied stress. In general, the strain at a given time after application of a uniaxial load (or deviator stress) will be greater a higher subfreezing temperatures. The creep rate at a constant deviator Stress will also increase with increasing temperature. Finally, it has been shown that there is a bflinear relationship between peak strength and void ratio for uncc ndersland' 196 ratio) there is increasing sand when friction b begin to contril 42 percent Sand in strength witl IgnorinS active zone, Whj three meters, th from close to th t00°C at some d This is illustra ture measurement Canadian North. 53’ the geotherma; siege of the temg lO ratio for unconfined sand—ice mixtures (Goughnour and Andersland, 1968). At lower sand volumes (greater void ratio) there is only a slight increase in strength with increasing sand volumes (smaller void ratios). Then when friction between the sand particles and dilatancy begin to contribute to the shear strength (approximately 42 percent sand volume) there is a considerable increase in strength with increasing sand volume. Ignoring seasonal temperature fluctuations in the active zone, which is limited to a depth of approximately three meters, the temperature in permafrost increases from close to the mean annual ground surface temperature to 0°C at some depth below the surface (Terzaghi, 1952). This is illustrated in Figure 1.3, which shows tempera— ture measurements at various depths in a borehole in the Canadian North. The increase in temperature is caused by the geothermal gradient that exists in the earth. The slope of the temperature variation depends on the thermal conductivity of the rocks or soil beneath the ground surface and the rate of heat supply. At an average, the temperature increases by 1°C for every thirty meters of depth corresponding to a thermal gradient of 30°C/Km, but Hm geothermal gradient can range from 10 to 60°C/Km. The average gradient for three mean annual ground surface temperatures is also shown in Figure 1.3. used in dynami vibration prob a line passing developed under Deming is prop loop and is usu etic damping rat 1 = .11 4n 1 invhich AL = area AT = area It is obvious th in the magnitude is determined, i heater the damp Both fie t“automate dyn i“he approxima ire applicable. tolather with th luring earthquak ll 1.4 Dynamic Properties of Unfrozen Soils As shown in Figure 1.4, most soils have non- linear stress-strain characteristics. The shear modulus, used in dynamic ground response analyses and foundation vibration problems, is usually expressed as the slope of a line passing through the ends of a hysteresis loop developed under symmetrical cyclic loading conditions. Damping is proportional to the area inside the hysteresis loop and is usually expressed as a ratio A. The hyster— etic damping ratio is defined as: AL A = m—T' (1.1) AL = area of hysteresis loop A = area of triangle OAB It is obvious that each of these properties will depend on the magnitude of strain for which the hysteresis loop is determined, i.e., the greater the shear strain the greater the damping and the lower the shear modulus. Both field and laboratory tests have been used to evaluate dynamic soil properties. Of significance is the approximate strain range over which the procedures are applicable. These ranges are shown in Figure 1.5, together with the approximate strain range experienced during earthquakes. As indicated on the figure, only Dlflrllionl {for larger Slim Modulus, 6 = 6 mm ratio, ll = AL ’t‘ urea oi hysteres' If mo of triangle Figure 1.4 HYSTI STRAJ I x 'I—- Gsophyslcal —-- i-Scrloco Wbrator h Vlbrotory 1 Plate Bearing esonont solid so * Flcld ** Laboratory Fllure l.5 FIELD STRAI Shann 12 Shear 62 Stress }} G r”-“- Definitions (for larger hysteresis loop) I ' AT Locus of tips of Shear Modulus, e: Gzll /’ "News" '°°ps Damping ratio, A: AL/47rA-r /’ AL= area of hysteresis loop AT: area of triangle 0A8 / _ Shear V B 7 Strain Figure 1.4 HYSTERETIC STRESS—STRAIN RELATIONSHIPS AT DIFFERENT STRAIN AMPLITUDES (after Shannon and Wilson, 1972) I I *- ‘-—- Geophysical————~) -)(— ‘- Surface Vibrator ——~>i 1 l ** T [rs—Cyclic Triaxial —-——>i -X* F— Cycllc Simple Shear—5i ‘ Vibratory l he ——*__*{ Plate Bearingj—‘U )4——-Torsiona s or Ffiesonant Frequencyyjé-x‘ (hollow samples) Resonant Freque n3“ solid samples) strong * Field Motion ** Laboratory is;— EARTHQUAKES lie—4 1 J, Io'5 Io'4 Io‘3 Ilo'2 Io'| I ' Io Shear strain—7, percent Figure 1.5 FIELD AND LABORATORY TESTS SHOWING APPROXIMATE STRAIN RANGES 0F TEST PROCEDURES (modified after Shannon and Wilson, 1972) of testing sci during strong- the test proce llilson (1972). In add values for sea relative densi shown in Figure the combined in of the form: G = 10( Which G = she c' = mea K = a f 2 and ”fitting ratios f4 it Shear strain Shear mo “mat extent b there is a signi inthe laboratory Net for these 'va l3 cyclic triaxial, simple shear, resonant frequency (hollow samples), and torsional shear tests are capable of testing soils within the strain range that occurs during strong-motion earthquakes. A description of all the test procedures indicated is given by Shannon and Wilson (1972). In addition to shear strain, the shear modulus values for sand are influenced by confining pressure and relative density. A typical relationship for sand is shown in Figure 1.6. In general, it has been found that the combined influence can be expressed by an equation of the form: G = 1000 K2 (“Ml/2 psf (1.2) in which G = shear modulus O$ = mean principal effective stress K2 = a factor relating relative density and strain amplitude Damping ratios for sands have been found to be influenced bY Shear strain as shown in Figure 1.7. Shear moduli for saturated clays are affected to a great extent by sample disturbance. Consequently, flmre is a significant difference between values measured in the laboratory and values determined in situ. To cor— rECt for these variations, laboratory values are L Figure 1.6 SHEAR (after 14 G =1000 K2(a;n')"2psf El Weissmon and Hort 096” A Richorf, Hall and Lysmer 0962) O Drnevich, Hall and Richorl 0966) 0 Seed 09680) A Silver and Seed 0969) V Hardin and Drnevich (ISTO) Sheor Strain-percent 75% Figure 1.6 SHEAR MODULI 0F SANDS AT A RELATIVE DENSITY OF ABOUT (after Seed and Idriss, 1970) ll.l .‘l‘.~ J1" ..... C VIC («CL—MI Emma 3350 Amwmc Doom 0:0 .525 Ahwmsgv. Eco 02:3! 62:94322 “.0005 20:21 uco :01 50.30.50 nnwms C~ULOI Coma $.01 USO COEnnmoss u “08015 8ka .mmZE ucm comm L913 ozocoo 1 ON «mam: comm nco $26 0 Romeo? Bo SE”; .ozfiaros o $me 75:95. 95 :oI £2550 o VN 8mm: EPSI a :8: toI nco 553.63 6 mN iuaaiad - ouoa buidwoo multiplied by It is believed with undrained shown in Figuri have been foum in Figure 1.9. Cyclic Cylindri cal sam- p . mung Pressure Planes at 45 dec woman)? horizc 1.10. The Princ ”Very ha mfrozen s Oi 1 ar fol 10Ws : E l dynamic = \ l6 multiplied by a factor of 2.5 (Seed and Idriss, 1970). It is believed that the shear modulus for clay increases with undrained shear strength at a given shear strain as shown in Figure 1.8. Damping ratios for saturated clays have been found to be influenced by shear strain as shown in Figure 1.9. 1.5 Fundamentals of Cyclic TTTT—TEIEEIET‘EE5Efifif—"T‘T' Cyclic triaxial testing involves subjecting a cylindrical sample in a cell to an initial isotropic con— fining pressure and then pulsating the deviator stress to cause a reversal of shear stresses which are a maximum on planes at 45 degrees to the principal stress directions (normally horizontal and vertical) as shown in Figure 1.10. The principal stress directions rotate through 90 degrees every half—cycle. Typical test results for an unfrozen soil are shown in Figure 1.11. From the results dynamic Young's modulus and damping can be calculated as follows: , 2] E . = [(0d comp. + 0d extention)/ (1,3) dynamic 8A A = L (1.4) _________________ 000 M nmwmz 000m DEC “3wa 9 Ahme C025) UCO COCCO£W§ “Nimm; C0m2>> UCO COCCOEW aklwmz ~L$O>00N Amwwmc mmtnu AmmmC 9.0.3... 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ZOHmMMNVZOU _H.N .wfiflmfi an Massage: 9H. mmHuH-ummmomm UHS‘ED NEH: DHB‘HUOWM‘ MHHZD “no.“ mmoaofih ZOHWMEZOU 9H0>GOO OB NI N ”Ag-H. 24 Hm\m ANM l boy H Dou— mA 13 undressed 02 8c Amemumflamoc 2:38 .2 Hmm.m Aoom\umoaflxv wcooow Mom nooMOHHx Aoom\exv cocoon Mom Hopoeoaflx Hmm.m floom\#wv ccooom mom comm Aoom\Ev Uncomm Mom muchae on ANE\ZUV Moose ouasvm Mom oonBocmmflm ANE\ZMV Hopes oumsvm Hem G0p3osoaflx m.m A E\zxv Hceoe mumswm “mm soesosoafix Aflmmv SUCH oucsvm Hog mossom m.n¢ N ANE\ZV Hosea mumswm Mom wsousos Amway uoow meadow Ham mossom mv.e sz wsouzac Ameav oosow cccom oco mate 3v: msmnmoix 3: messed v.0H AmEOV muapaeflpgoo Denna Ass 50V monocfl OHQSU Mmo.o “Nev muouoe oswsgm “em wmv poem seesaw mv.m ANEOV muauaeflusoo onmagm Asa Wmv masocfi meadow moms c5 38% St #8.“ vmmo.o AEV nuance Acflv masocfl ovm.m AEoV mnouoEflyqao ACHV menace 3 mamauaos OB uum>soo OB WMHBMMAOMm UHE¢ZMQ EBHB QMBZOU N.N quflB In thi was obtained f Dynamic shear Young's modul tionship: in which Edyn to allow this for ice and fro tors' work are ratio was not dI tested in this 1 2.1.2:: 959; Seismic 51816 technique lie and frozen c Shear wave veloc millod, elastic 1Nation and the l‘ M the source “mgraphs or 25 In this research program, dynamic Young's modulus was obtained from the cyclic triaxial tests performed. Dynamic shear modulus can be evaluated from dynamic Young's modulus for an isotropic material using the rela- tionship: Edynamic G: W (1.5) in which’ _ ' l Edynamic — dynamic Young s modulus u = Poisson's ratio To allow this conversion to be made, Poisson ratio values for ice and frozen clay obtained from other investiga— tors' work are also presented in this chapter. Poisson's ratio was not determined for the ice and clay samples tested in this research program. 2.2 Previous Methods to Evaluate Dynamic Properties of Ice and Frozen Clay Seismic methods have been the most widely used field technique to determine the dynamic properties of ice and frozen clay. Specifically, the compression and shear wave velocities can be determined. In the seismic method, elastic waves are produced by a source at a known location and the waves are detected at various distances from the source by vibration sensitive detectors called seismographs or geophones. (The source of the waves is usually an e distances, bu hammer can be instant of ti can be observe distance from muted. If materials are the substrata be determined travel time oh seismic method In 196 ice and frozen ing beams of fn thematic diagr. Piwure 2.1. mm 27.94 cm. Perm "ite frozen at e "He vibrated b3 Thames that I @hcted by the “he: end of the ile°tromagnets n 111the longitudi mimic properti 26 usually an explosive charge for measurements over great distances, but for a short distance the impact of a hammer can be used.) The waves are produced at a known instant of time so that the travel time of propagation can be observed. Knowledge of the travel time and distance from the source allows the wave velocity to be computed. If the seismic wave velocities for given materials are known, then information on the geometry of the substrata of the earth's surface at a location can be determined by an interpretation technique from the travel time observations. A complete treatment of seismic methods is given by Dobrin (1960). In 1969, Kaplar determined dynamic properties of ice and frozen clay samples in the laboratory by vibrat— ing beams of frozen specimens with electromagnets. A schematic diagram of the test apparatus is shown in Figure 2.1. The beams were approximately 3.81 x 3.81 x 27.94 cm. Permanent bar magnets, 0.476 x 0.476 x 5.08 cm, were frozen at each end of the specimens. The specimens were vibrated by the electromagnet mounted at one end. The waves that propagated through the specimens were detected by the electromagnet which was mounted at the other end of the specimens. The orientation of the two electromagnets was the same. The specimens were vibrated in the longitudinal, flexural and torsional modes and the dynamic properties could be evaluated at the resonant 27 Amom— .Lm—amx Lopwmv moe zucwzaucu Hmmh quo onH Qmumom mo UHHCD 5:03:00 3:63:33 Eozom 025 3:075» 5:05:00 no» 'l/ 25:09 AEotom. .954 :05 .Eonuomv r/ansoco mtamnwta 30.: - / “83:85.33... 3295.283 the longitudii to measure the two accelerome longitudinal c The driving mc was at resonan ing varied fro Young's modulu (G*), damping were Obtained 33 the longitudinal response and two on the circumference to measure the torsional response. At the base plate, two accelerometers were attached for measuring the longitudinal or torsional sinusoidal driving motion. The driving motion frequency was varied until the sample was at resonance. At resonance the frequencies of test- ing varied from 1 to 1000 kHz. The complex dynamic Young's modulus (E*), complex dynamic shear modulus (G*), damping (tan 6), and complex Poisson's ratio (u*) were obtained from the test program. 2.3 Dynamic Elastic Properties of Ice _________________________________________ Considerable progress has been made in recent Years to determine the dynamic elastic properties of ice and a substantial effort has been made to compare the dynamic elastic properties from field and laboratory tests. Most of the field work has been done on the Greenland ice sheets. The laboratory work has been con- ducted on artificial frozen samples and ice cores from Greenland. Several parameters influencing the dynamic elaStic properties have been identified and investigated. The most important appear to be temperature, density and frequency. The influence of strain amplitude and con— fhfihg pressure apparently has not been reported. 2.3.1 Effect The i moduli has be summarized by 2.6, 2.7, 2.8 the temperatu: compression we COmpression we P10tted as a 1 of ‘50°C the v decreases to a The velocity d about 3.68 km / temperature ra velocity appea and the rate 0 ture range ‘20 of temperature wave velocity :. l ..68 kin/Sec at 34 2.3.1 Effect of Temperature The influence of temperature on dynamic elastic moduli has been reported by several investigators and summarized by Roethlisberger (1972), as shown in Figures 2.6, 2.7, 2.8 and 2.9. The figures illustrate that as the temperature approaches the freezing point shear and compression wave velocities decrease. In Figure 2.6, compression wave velocities froni many investigations are plotted as a function of temperature. At a temperature of -50°C the velocity is about 3.88 km/sec, but it decreases to about 3.85 km/sec at a temperature of —20°C. The velocity drops rapidly from 3.85 km/sec at -20°C to about 3.68 km/sec at the melting point. For the lower temperature range —20 to -50°C, the compression wave velocity appears to decrease linearly with temperature and the rate of decrease is smaller than for the tempera- ture range —20 to 0°C. Figure 2.7 shows the influence of temperature on the shear wave velocity. The shear wave velocity is about 1.94 km/sec at —20°C and about 1.68 km/sec at the melting point (for samples taken from various Mountain Glaciers). As the melting point iS approached, the velocity drops very rapidly as shown in Figure 2.8. As shown in Figure 2.9, the sound velocity in SYnthetic ice cores is almost constant at about 3.5 km/sec in the range of temperature -20 to —4°C. ii P—WAVE VELOCITY, hm/tec VP, Lani \D 38; b/ um N 0——m0 - 0. ’.~' 1‘. ‘(fi C7 9' so km/sec \fla=-2 3msec" (°C)_' dT 38 V , P-WAVE VELOCITY, 0 4W3” ‘40 . r, TEMPERATURE.°C Seismic measurements: 1. Greenland ice sheet, Brockamp et al., 1933; after Thyssen, 1967. 2. Greenland ice sheet, Joset and Holtzscherer, 1954. 3. Baffin Island, Roethlisberger, 1955. 4- Greenland ice sheet, Bentlev et al., 1957. 5} Novaya Zemlya, Woloken; after Thyssen, 1967. 6. Greenland ice sheet, Brockamp and Kohnen, 1965; after Thyssen, 1967. 7. Ellesmere Island, Hattersley—Smith, 1959; Weber and Sand— strom, 1960. 8' Edge of Greenland ice sheet, Roethlisberger, 1961. 9- Edge of Greenland ice sheet, Bentley et al., 1957, Gold- thwait, 1960, 10- Antarctic Peninsula Plateau, Bentley, 1964. 11- BYrd Plateau, Bentley, 1964. Ii. Victoria Plateau, Bentley, i964. . Polar Plateau Bentle 196 . . 14- Various Mountain glaciers: a) Thyssen, 1967; b) Vallon, 1967,- c) Clarke, 1967. Ultrasonic measurements: Line A Robin, 1958; .Point B Bennett, 1972; Point c Thyssen, 1967; Line D Thyssen's empirical relationship. Figure 2.6 P—WAVE VELOCITY OF ICE VERSUS TEMPERATURE (after Roethlisberger, 1972) h- . ||||1J|_|_d|b _ 2.0 a 4. . l . _ ”1?er V'LLO 3 8 T 0 0 9 7 SI! Brc . . 6 8 uouxEx .>.r_oo._m> m><>> m<31A .1) Figure 2.7 1 Figure 2.8 M 36 2.0 1 . I l T l I A. ULTRASONIC MEAS. Bennett (I968) =-Linlsec4(°C)” dT LB _ SEISMIC MEASUREMENTS — I ' Greenland Ice Sheet, Josei and Hoiizscherer (i953) x0 2 0 Greenland Ice Sheet, Bentley et al (l957l 3 I Antarctic Peninsula Plateou‘Behrendlil964) L7 4 DByrd Plateau, Thiel et al “959) 5 A Ross Ice Shelf. Thiel and Osienso(i96il 6 A Filchner Ice Shelf, Thiel and Behrendtil959|9590l Vs, SHEAR WAVE VELOCITY, km/sec 7 X Various Mountain Glaciers a, Fdrtsch and Vidal (l956) "b b Vallon(|967l I.6 J L l J l L o 40 -20 ~30 T, TEMPERATURE, °C Figure 2.7 S-WAVE VELOCITY OF ICE VERSUS TEMPERATURE (after Roethlisberger, T972) _I_ - . - - 7’ .T._.._...r..._ E 40 vmfl‘rr o;b°’:v°’o’ ‘3”? ‘VV; ni‘;*'°lo_o 9 a ”a E Vie/if. 5»... ° - __ .._—-f.--._._on__n——— “‘ / a Parallel to c- axis ). I: U o 39‘;- .1 m > LIJ > <1 _ _)__...: .:_. 3 3sfyL—1‘J'~W’LJVJ:——‘#—AI 0': b Perpendicular to c 0an i _ , _-,. V i l 37 0 I- ”,I ,-“u I_M 4 "I .2 - I" TEMPERATURE, °C Figure 2.8 P-NAVE VELOCITY IN THE PRINCIPAL DIRECTIONS OF SINGLE-CRYSTAL ICE VERSUS TEMPERATURE (after Brockamp and Querfurth from Roethlisberger, 1972) .. -_.. Figure 2.9 muo‘ T 15» 1c: Figure 2.10 SL ME 19 IIIIIIIIIIIIIIIIIIIIIEIIII:TTTTTTTTTTTTTTTTTTTTT_________TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT“:“43:==T"'"'TT" 37 "Inc km/sec *5 r r l T I4 _ 4.0-— l2- WG-0 35‘ ICE ,, .. p. 910'- 3.0” o J i- U ’ s— 2.5- 2.0- 6— P" '1 ' l l l l "'1 -5 -l0 -l5 -zo rzupsnaruns. -c Figure 2. 9 SOUND VELOCITY IN SYNTHETIC ICE CORES VERSUS TEMPERATURE (after Muller, 1961, from Roethlis— berger, T972) D $01.10 r‘rtrj rrrri[TFrl[rr1r , cucin '10 l ’0 Ice //”*’9 cnouwo xc: (You 09 R Icg// Inoss 1c: SHELF I50- sci-menu.) _ __ __ ————————— x— LAEE/ ,,-_x ————— x cue/5n ms 5 en 1c: " / GLIEIER lCEllv at 7 200mm cum) / GLACIER xc _ I2.0 .. / IGREENLAND 11:: 3.5 —- 1c: , MtE Item + V .. A 0mm ICE schr - L ”.0 VL Im/sec) " (tr/sec) __ uxc s ” IODSILABI y no; PRESENT STUDY oanONML BEA!“ qurlCALLy—z— . i" 5; Mn “WA ICE ’IT 4" Io.o 3.0 r'? NOR/IONT‘L“ L E G E N D A JOESYING 95 "' 0 er do: :95. o WOLCIEN. u gum .95‘5' ‘ p was". l95 x nos u. one :95: A hELLBARDY [955 o BENREHDT. i964 q anocx'mvu'ui. :93: o u we .r cl, :9; a HIEL IV l ‘95! Q NOITNL SEE~GER 0 5'":ch 1959 I '96I + BOVLE B SPROULE is): liliIliliJl.L4_.LIilii[9° 0 -IO ~20 -30 -40‘C L 1 l l I l J l I l l l I l l 1 I l l 32 is 0 -l6 -32.; T E M P E I A T U R E Figure 2.]0 SUMMARY OF LONGITUDINAL WAVE VELOCITIES IN ICE MEASURE BY VARIOUS INVESTIGATORS (after Kaplar, I969) The may be expre units (meter perature coe compression cates that th wave velocity decreasing te temperature c appropriate f determined th saIllllles of frc Stillmarized the and those of c Presented indi sheets and gro determined in concluded that "htther labora affected by tel 2.3.2 Effect ( Conside 8ice of ice deI i°ethlisberger from many inves —7——r~——WT 38 The influence of temperature on wave velocity may be expressed by a "temperature coefficient" with units (meters/second)/°C. Robin (1958) reports a tem- perature coefficient of —2.3 (meters/second)/°C for compression wave velocity. Roethlisberger (1972) indi— cates that the temperature coefficient of the compression wave velocity decreases in its absolute value with decreasing temperature and he also suggests that a temperature coefficient of —l.l (meters/second)/°C is appropriate for the shear wave velocity. Kaplar (1969) determined the dynamic elastic moduli of artificial samples of frozen ice and natural ice cores. Kaplar summarized the influence of temperature using his tests and those of others as shown in Figure 2.10. The data presented indicates that the field velocities of ice sheets and ground ice are higher than the velocities determined in the laboratories by about 20%. Kaplar concluded that the dynamic elastic properties of ice, whether laboratory frozen or natural, appear little affected by temperature. 2.3.2 Effect of Density Considerable work has been reported on the influ— ence of ice density on dynamic elastic properties. Roethlisberger (1972) compiled field and laboratory data from many investigators and corrected these data to —16°C based on a tl /°C. The re: fall within a wave velocity sity of ice. sec at 0.92 g This band in of ice is si In a velocity of i determined by refraction se tions in the results employ in Figures 2.] of compression The compressic sec at 0.90 g/ shear wave vel “~90 g/cc to a lion and shear from 0.90 to 0 “it! velocities greater for de: lilies above tl 39 based on a temperature coefficient of —2.3 (meters/second) /°C. The results are shown in Figure 2.11. The results fall within a relatively narrow band. The compression wave velocity of the band varies linearly with the den- sity of ice. The velocity decreases from about 3.83 km/ sec at 0.92 g/cm3 to about 3.38 km/sec at 0.76 g/cm3. This band indicates that the compression wave velocity of ice is significantly influenced by the ice density. In a study conducted by Bennett (1972), the velocity of ice cores from Greenland and Antarctica were determined by ultrasonic methods and, in addition, refraction seismic surveys were conducted at the loca— tions in the field where the cores were taken. The results employing these two test methods are presented in Figures 2.12 and 2.13. The figures show the variation of compression and shear wave velocities with density. The compression wave velocity varies from about 3800 m/ sec at 0.90 g/cc to about 1100 m/sec at 0.40 g/cc. The shear wave velocity varies from about 1800 m/sec at 0.90 g/cc to about 520 m/sec at 0.40 g/cc. The compres— sion and shear wave velocities decrease almost linearly from 0.90 to 0.6 g/cc. At densities lower than 0.6 g/cc, the velocities drop rapidly. The rate of decrease is greater for densities lower than 0.6 g/cc than for den- sities above this value. ‘2 3“]!!! Una nEeixookm a: .50 3:30:30”. afloat—an no. 5 039—. no uwufloaoun 00— no» vagina—.8 .9301; Esq—0.00:5 i ANNmF .tmmtonmwpcpmom at... Emzmo may... we. .0 E03... .23-.. :.N 8.5: .Uo\A©coomm\meon. m.Nl mo #Goaoawwwoo ousumuwmfion m :0 comma vocal . . Cu. UGHUGHHOU THUG HHfl " mn¢OZ "so; .5522... .Q «mo mmd v00 omd wNo on A652. 9:3 1.23:0: use 1.2.53 0 3.59.55. 2:. 2.3.520 :8: 3.8 1 mm 4 co mnemEo.=m$E .o .mnEsc wmzw. m .0 new... . 32.55 .o 33 .2..2.Ecanm It . Agocxcs .36...ch message... 08 2. 29:3 305.. £53. rdA mcwEEwam 30:22.... £53. 0 2.2:...QO cognacmgn .Awmm: :33. .0 San .SSEtoaum o . Am. 2.5. 32:25 E... 2. 2.5. 5.3.26. 2:. aEaqum .3 .2“. 2.56580 325.2 .2 5 v35. .0 25.2.0... co. .8 @3258 .3622. 32.3.82... i 'AliOO'IBA 3AVM—d OBS/WK o 5 I u I 2 ILi~iLI. Lillgi,i,li » \ MN I .AIV 8 6 ‘Iilii .Ii 2 I O 2 mi hie-05:330. $1.300} U.IQI)O XHJQSXUU o0 Btbou hi 9 no. .04 hIII 43 . m/sec ' VELOCITY souo CIRCLE poms OBTAINED USING ROBIN'S [MPIRICAL FORMULA v. - "32‘5" (I-ooooem . 10‘ l l I I 1‘ l l J L 0 4° 80 I20 I60 200 D E P T H , m iigure 2.14 P-WAVE VELOCITY OF ICE VERSUS DEPTH AT CAMP CENTURY (after Clarke, I966) :c l. I l l I I I I I I r I PIO_BBMC 8 fl E Q a n U C U j" 6 e ___5522.»L~—~'t"‘“" —————— o ‘ . O .' o .J 3 8 4 ° 2 ‘5’ p-0.88 O < ._,__._———-°"—"‘ 2 o > , o x u .1 g . ° 8 2... o p-O.72 fi/ '0 o ‘fo ‘ C o O u (0) E'Younq's (o) G' Shear t I I l I 1 i I L A 4 400 800 I200 ISOO 2000 2400 2800 FREOUE NCY cps . Ire 2.15 COMPLEX DYNAMIC MODULI 0F ICE VERSUS FREQUENCY (after Smith, 1969) -(I slightly wit 2.15. The c plotted agai The rate of complex Shea M4 Effec- Info: on dYnaInic ej (1972) C0Ddu< cores and 3e]- locations Whe Figures 2,12 Compression t cantly diff er the ice Was 3 Roethlisberge is to re duce bUbbly ice. 1 Pression Wave thata Slight with increasi] for this state v , 44 tly with increasing frequency as shown in Figure The complex dynamic Young's and shear moduli were ed against frequency over a range 800 to 2800 cps. ate of increase of the complex Young's modulus and ex shear modulus are nearly identical. Effect of Confining E Information on the effect of confining pressure amic elastic properties is very limited. Bennett conducted ultrasonic tests on unconfined ice and seismic surveys were performed in the field at ons where the cores were taken. As shown in 3 2.12 and 2.13, the results from the unconfined ‘sion tests on the core samples are not signifi— different from the seismic survey results where was subjected to the in situ confining pressure. sberger (1972) reports that the effect of pressure duce porosity and, hence, increase the density of 'ce. With increasing density the shear and com— wave velocities should increase. He states light increase in velocity should be expected reasing pressure, but provides no justification statement . Smit the damping presented thi (tan 6/2). (1) '. f1 Va fa IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIEEZT'TTTTTTTTTTTTTTTTTTTTTTTTTZZTTTTTTTT Smith (1969) studied the parameters influencing ping properties of snow and ice core samples and ed the test results in terms of a loss factor 2). (l) (2) 45 2.4 Damping of Ice His work indicates: The loss factor appears to decrease with an increase in frequency but the trend is not well established because considerable scatter exists in the data as shown in Figure 2.16. The density of the ice sample was 0.72 g/cm3. The loss factor varied between 0.01 and 0.07 when the frequency increased from 800 to 2400 cps. With increasing driving force, the loss fac— tor tends to increase, but again the trend is not well established owing to the scatter of the data as shown in Figure 2.17. The density of the ice sample was 0.72 g/cc. The driving force was expressed in accelera— tion voltage output (RMS) at the sample base. When the acceleration voltage was increased from 0.01 RMS to 0.05 RMS the loss factor varied between 0.01 and 0.07. The most significant influence on the loss factor is density. As shown in Figure 2.18, 0! 8 (Ian /2)L W (MN 8/2)T IIYTT 0 T] T "L' (ON "TIME 00! 600 8( Figure 2. 0 I T‘r'll ("ms/2)L and V” 8/2)T Figure 2.17 46 I I I I I I . 0 0° . I 0° '. 0° 0 o ., .. ."LuhI Longitudinal III-"I” AV9:0 0356 "T"(o) Tomonol 00 T (0) “9:0 0298 I I J n I l I I200 I400 I600 I300 2000 2200 2400 ) 800 I000 FREQUENCY cps ' Ire 2.16 LOSS FACTOR 0F ICE VERSUS FREQUENCY (after Smith, I969) OJ 77 , ' -072 ) o o o o P L o I °. ,. . , ° °& .. T - . LIU , .o .9- "wo, . on: I" 1 . J . o 00: 002 003 004 005 006 ACCELERATION VOLTAGE OUTPUT RMS AI Sqmple 8059(Gain=100) LOSS FACTOR OF ICE VERSUS DRIVING FORCE (after 2.17 Smith, 1969) ( A.OCO.ICO.P~ m COL. 9 I 2 e r U 9 -I F 32;»)...SJ v ”SF IOFUQU mmOJ wodmw>< Figure 2.] » tcc .A ~\.wco; '- 47 2 004 ’53 I I I I I I ~ ao\ C o C; 0.03 I O +- 2 u. 002 w w 3 L=LongIIudmol 0 I 3 O T=Tors:onol 4 (I lu 2 o I 1 L 1 1 L 04 05 06 O7 08 09 DENSITY, g/Cm3 ‘e 2.I8 LOSS FACTOR OF ICE VERSUS DENSITY (after Smith, I 3 OIZ v f I j ‘r r f 1 T I r I I I 2 G 3 '- 0.08 § Ice 00 0.04 /‘ - .9 L I I J 1 I L I L I J I ;L ‘IO IO 20 30 4O 5O 60 O. 0'2 f‘l T rfi r I I T I I I 17 Tan 8 (Torsional) .0 o . . _ \ 20 3O 40 50 60 Temperature. 'F 2.I9 EFFECT OF TEMPERATURE ON TAN6 OF ICE (after Stevens, I975) Step ture on damp temperature shown in Fig to 0.06 at 2 is 0.013 at sional vibra. 48 the loss factor is 0.04 at 0.4 g/cc but drops to 0.005 at a density of 0.9 g/cc. Stevens (1973) studied the influence of tempera— damping of ice. His work indicates that as the ture increases the damping (tan 5) increases as 1 Figure 2.19. Tan 6 is 0.045 at O°F and increases at 25°F for longitudinal vibration whereas tan 6 i at 0°F and increases to 0.06 at 25°F for tor— ibration. 2.5 Dynamic Elastic Properties of Frozen Clay Most of the work to evalutate the dynamic elastic as of frozen clays has been in the laboratory. -y, the only in situ measurements were reported (1963); the shear wave velocity of alluvial clay 'ay, Alaska, at —2°C was 7.8 kilo ft/sec. A num- vestigators, using different laboratory testing 5, have found that the dynamic elastic proper- rozen clay are apparently dependent on the fol— :tors: void ratio, ice saturation, temperature, and dynamic stress and/or strain. 'ect of Void Ratio e effect of void ratio has been studied by 973). He indicates that as the‘void ratio of y increases beyond 1.0 (i.e., the volume of ice becomes frozen clay) approach the Miller (1961 of -10°C, th increases ab 67% to 96%. 2.5.2 Ef W \ It i PIOperties o; be dependent to cement the ExPressed in is the ratio the Voids in St‘eVens (1973 decreasing ic constant on a is Plotted a9 1030f Suffie 0.075 GN/m2 a i 2.5 w 49 res significantly greater than the volume of ay) the dynamic elastic modulus tends to that of ice. Similar results were obtained by 961) as shown in Figure 2.20. At a temperature the sound wave velocity of frozen clay cores about 20% for an increase in porosity from Fect of Ice 1 . is generally believed that the dynamic elastic of frozen clay at a constant void ratio should nt on the volume of ice in the voids available the soil grains together. This can be in terms of the degree of ice saturation which .0 of the volume of the ice to the volume of .n a soil mass. As shown in Figure 2.21, 73) found that the decrease in modulus with ice saturation for Suffield clay is nearly a semi-logarithmic plot. The ice saturation against the log of dynamic complex shear modu- Leld clay. The modulus increases from about at 0% ice saturation to 1.14 GN/m2 at 100% Lon. !t of Temperature dynamic elastic properties of frozen clay ease with ascending temperature. At —— II/s TY VELOCI Figure 2.20 50 fI/sec km/sec HO 4-5 I r 1 I I4 40 I2 15 >. p.— _ 96% U '0 3.0 tat—1+1," O CLAY and ICE " (mixture II] > 8 Z5 / 2 O / s ‘(/ I I J L50 —5 40 —5 ~20 TEMPERATURE,°C SOUND VELOCITY IN SYNTHETIC FROZEN CORES AT TWO POROSITIES VERSUS TEMPERATURE (after MuIIer, 196I, from RoethIisberger, 1972) U Figure 2.: “911m 222 “gaa‘ ....~._.p- - 51 Point Non~frozen Soils. WC. Design. f=lkHz (70:34.4kN/m2 °/. Point . f Temp DeSIgni Frozen SOIIS ] KHZ °C G Suffield Clay I —9,4 'III I'IT'I'] I'r'III Ice Saturation, °/. (3‘ Complex Shear Modulus, GN/rn2 e 2.2I EFFECT OF ICE SATURATION 0N COMPLEX SHEAR MODULUS FOR FROZEN SUFFIELD CLAY (after Stevens, I973) as . . . , . , fl 0 20-30 Ottawa Sand 2‘4 (p=2.19 q/cm3) fl E ’- 2'2 Hanover Silt .2? Ip= 1.83 g/cm3) O 3 2.0 § A A A A A A 1.8 Goodrich Clay 4 (p=l.Slg/cm3) LG I I l L L 4L I ' 6 -l2 '4 O "8 Temperature. "C 3.22 S-WAVE VELOCITY VERSUS TEMPERATURE FOR FROZEN GOODRICH CLAY (after Nakano and Fraula, I973) temperatures temperature determined t afunction c The results have velocit lm/sec at -1 Kapl niInes, test frozen Fargo 2'23~ The p- from 5.5 x ll 30°F Whereas Clay drops f1 Iii/Sec at 30. Steve column tes ts, 52 tures near 0°C, the decrease with increasing ture is fairly rapid. Nakano and Fraula (1973) led the shear wave velocity of Goodrich clay as Lon of temperature using ultrasonic techniques. Ilts are presented in Figure 2.22. The shear .ocity is 2.0 km/sec at —l6°C but drops to 1.7 t -l°C. Kaplar (1969), using resonant frequency tech— tested beams of frozen Boston blue clay and argo clay. The results are presented in Figure 1e P-wave velocity of frozen Fargo clay drops X 103 ft/sec at -lO°F to 3.2 X 103 ft/sec at "eas the P-wave velocity of frozen Boston blue 3 s from 10.3 x 103 ft/sec at -10°F to 6.4 x 10 30°F. tevens (1975), using forced vibration resonant StS, studied the influence of temperature on :lay. The results are shown in Figure 2.24. .C complex Young's modulus drops from 1.7 X 107 ' to 5.5 X 106 psi at 30°F. The dynamic com— ‘modulus drops from 6 x 106 psi at 0°F to Psi at 30°F. Stevens indicates that tempera— greater effect on fine—grained soil (clay) arse-grained soil (sand). Ller (1961) determined the sound velocity of ' cores as a function Of temperature as Shown n.’.4\p.-.. - Inlmno ‘44-”: L ONGI Ya vL, LONGITUDINAL WAVE VELOCITY. "no: “u LonaIruomAL wAv: VELOCITY. fl/Ilc o TEMPERATURE.“ LONGITUDINAL WAVE VELOCITY VERSUS TEMPERATURE FOR FROZEN BOSTON BLUE CLAY AND FARGO CLAY (after KapIar, 1969) E ~e...- _ _ N.e»~.- L \Le.-~e \ la‘nlv 2n 0.10 W m 9.. ~00 .OQ.JDOQ¢ XOR-E00 “Ow-.0 ”to AtelU WC W... .I T—LLLIEIEFI— . n10 .mlu 3 Design, ' SW °/o "/o 30 96.9 ‘— 0.83 G d h CI Sb -9 .4 00 rIc 0y '07. I ~ ' 3a to6 . . \ \ 3a \\ as I 3b \. 3b x. l O 0 IO 20 30 4O 50 60 Temperatu I 9. °F 4 EFFECT OF TEMPERATURE 0N COMPLEX MODULI OF FROZEN GOODRICH CLAY (after Stevens, I975) in Figure 2 drops from at -lO°C. velocity dr 1.75 km/sec decreases o '20°C. Ian dynalllic 91a: able. Steve modulus of s quency. At inane 00m; from 1.83 x 1012 Whereas Manchester 3 1'4 X 106 p3 55 re 2.20. At a porosity of 67%,_the velocity rom about 2.7 km/sec at -20°C to about 2.6 km/sec 2. For the temperature range -10 to -1°C, the significantly from 2.6 km/sec at -10°C to ”see at —1°C. ( drops At a porosity of 96%, the velocity as only slightly in the temperature.range -4 to ffect of Frequency __________________ Information on the influence of frequency on the elastic properties of frozen clay is not avail— :evens (1975) indicates that the dynamic shear >f silt and sand increases with increasing fre- At 25°F and a dynamic stress of 0.1 psi, the omplex shear modulus of Ottawa sand increases x 106 psi at 1 kHz to 2.02 x 106 psi at 103 as the complex shear modulus of frozen Hanover— r silt increases from 1 X 106 PSi at 1 kHz to pSi at 1000 kHz. Stevens notes that the rate :e is greater in the range 1 kHz to 5 kHz. 'ect of Unfrozen ent kano and Fraula (1973) suggest that a strong n exists between the dilatational wave velocity frozen water content. Figure 2.25 presents the an experiment in which the dilatational wave .C§.COU :10; CO~OC;C3 a! 5 2 2 e “I. U 9 II F >O.U >50 O\..0.0.$ O q water/q dry clay w Unfrozen Water Content 9 0.1 56 .N 5" o o Dilatational Wuva Valocity Inn/a o V w Unfrozen Water Content T Temperature c‘C DILATIONAL VELOCITY AND UNFROZEN WATER CONTENT VERSUS TEMPERATURE (after Nakano and Fraula, I973) velocity an were measur content dec increases. ing a freezl to be cause. Based on the state, "the re content is g the dilatati 2'50 Effec Sim The dynamic e 1&8 able' SteVe and Sand dec effect is gr frequenCy. complex SIIGQ: from l~82 X . 1.79 x 106 p ITOm 0‘96 X ] 0'94 X 106 PS 57 and unfrozen water content of a Kaolinite clay sured simultaneously. As the unfrozen water decreases the dilatational wave velocity 5. The observed hysteresis in the velocity dur— eeze-thaw (cooling—heating) cycle is believed used by the hysteresis of unfrozen water content. the results of this experiment,Nakano and Fraula here is very little doubt that the unfrozen water is a major factor contributing to a variation of :ationalwave velocity with temperature." ffect of Dynamic 3r Strain) The effect of dynamic stress (or strain) on the elastic properties of frozen clay is not avail- :evens (1975) reports that the modulus of silt decreases with increasing dynamic stress. The greater at higher temperature and at lower - At 25°F and a frequency of 1 kHz, the dynamic hear modulus of frozen Ottawa sand decreases X 106 psi at a dynamic stress of 0.10 psi to 5 pSi at a dynamic stress of 5 psi. The dynamic rear modulus of frozen Manchester silt decreases x 106 psi at a dynamic stress of 0.10 psi to ‘pSi at a dynamic stress of 5 psi. III Dam; reported by Figure 2.26 tan 0. At ; 0f Goodrich 35°F for lor zen clay inc torsional vi frozen state The ClaI is not on tan 5 of (1975) indie. strongly inf; Lhere was a ( in the 1‘0 k} stress of 5 I from 0.051 at honey of 10 frozen Manche honey 0 f 1.0 t . orstonal Vib 58 2.6 Damping of Frozen Clay _________._________________ Damping of frozen clay in terms of tan 6 has been :ed by Stevens (1975). Stevens' work, as shown in a 2.26, indicates the effect of temperature on At 1 kHz and a dynamic stress of 0.1 psi, tan 6 drich clay increases from 0.07 at 0°F to 0.10 at or longitudinal vibrations. Tan 6 of the same fro— ay increases from 0.06 at 0°F to 0.11 at 25°F for Ial vibrations. Tan 6 appears to be higher for the state than for the unfrozen state. The influence of frequency on damping of frozen not available. However, the effect of frequency 6 of silt and sand has been reported. Stevens indicates that tan 6 of frozen silts and sand are y influenced by the frequency. He found that as a decrease in tan 6 with increasing frequency L.O kHz to 10 kHz range. At 25°F and a dynamic >f 5 psi, tan 6 of frozen Ottawa sand decreases 51 at a frequency of 1.0 kHz to 0.025 at a fre- f 10 kHz for torsional vibrations. Tan 6 of anchester silt decreases from 0.069 at a fre- f 1.0 kHz to 0.048 at a frequency of 10 kHz for I vibrations. Ipparently, no work has been reported on the 5 dynamic stress (or strain) on damping of frozen Levens (1973) reports the effect of this variable .- FIgure 22' 59 IIII O h) .4 ._I ‘1 —I .J _l -I m8 (Longitudinal) .0 o '. a: 0.04 1 1 I I l I 1 l I l I I I I ‘I0 IO 20 30 4O 50 60 O. 0J2 r I I I I I I I I I I I I i5 _g 0.08 3 E (00.04 _—-—-_--I. .5. I n 1 I 1 'IO 0 IO 20 3O 40 50 Temperature , 'F e 2.26 EFFECT OF TEMPERATURE ON TAN6 0F FROZEN GOOD- RICH CLAY (after‘ Stevens, 1975), III on frozen relatively increases : kHz and -3. from 0.069 35 kN/mz. Ste Gently affe decrease in damping Of 60 frozen silt, however, and indicates there is only a Itively small increase in tanISas dynamic stress eases for frequencies between 5 and 10 kHz. At 1 and -3.9°C, tan 50f frozen Manchester silt increases 0.069 at a dynamic stress of 0.9 kN/m2 to 0.79 at d/mz. Stevens (1973) found that tan 6 is not signifi- .y affected by void ratio. There is only a slight ase in tan 6 as void ratio increases. Generally, ng of frozen clay is greater than that of ice. 2.7 Poisson's Ratio of Ice and Frozen Clay Poisson's ratio is defined as the ratio of unit 11 strain to unit longitudinal strain, under the :ion of uniform and uniaxial longitudinal stress the proportional limit. Poisson's Ratio of Ice Kaplar (1969) computed Poisson's ratio of ice 1e relation: _£_ “"2G 1 (2.2) E = dynamic Young's modulus G = dynamic shear modulus His result ice varies whereas Po: varies witl shown in Fj that Poissc mately 0,33 033. The deduced fro sonic labor and were pr« 2'23- The I ratio is bet influenCed I reTorts the indicate a d This is Show that the Val 61 3 results indicate Poisson's ratio for artificial frozen 2 varies with temperature from about 0.33 to about 0.41 areas Poisson's ratio for Portage lake (natural) ice 'ies with temperature from about 0.28 to about 0.36 as wn in Figure 2.27. Roethlisberger (1972) suggests t Poisson's ratio of bubbly ice and snow is approxi— ely 0.33. The influence of density is approximately 3. The influence of density on Poisson's ratio, Iced from seismic, in situ measurements and ultra— .c laboratory studies, were summarized by Mellor (1964) were presented by Roethlisberger, as shown in Figure . The summary of results indicates that Poisson's 3 is between 0.25 and 0.30 and is apparently not Ienced by density. In contrast to this, Smith (1969) TtS the results from forced Vibration tests which :ate a dependency of Poisson's ratio on density. is shown in Figure 2.29. Smith comments, however, the values appear to be unreasonable. Poisson's Ratio of 1 Clay Based on longitudinal and flexural vibration Poisson's ratio for frozen Boston blue clay and .Fargo clay has been reported as a function of ature by Kaplar (1969). The results are shown in 2.30. Poisson's ratio for both clays is about t longitudinal vibration and 0.2 for flexural “Ute: Up on Sl’ITbI 2 | I II 62 oserTII IIIIrTrIIIIII [ / I artificially irozenice Haj = —I o It T‘s—fifi—I POISSON s RATI IL 2% °J o fi—I—I—mA—w—rfifii Wigs‘ Q 4 l x I>> I II; a 0‘ [1' Mk— I ' A 0:10 xxx I *“*tfi , I>>I [>54l flk" Ia - g en. 05 I I I T 7 . I T I r 1 I’T’T W I V V I I I Portage Lake (natural) Ice 0. l . , _ POISSON’S RATIO, I“ % —I IIJILLIII IIIL O I TEMOE PATURE . °F Open symbols indicate flexural vibration and closed symbols indicate longitudinal vibration. e 2.27 POISSON'S RATIO OF ICE VERSUS TEMPERATURE (after Kaplar, I969) 9 2 2 e r U - n [I 0| Figure 2.. 7.. 0 073;; m. 20mm.0& 63 9 p. <1 I: fl) 2 o . U! ‘1’ O 1 I — Eur/e] 1' _a_/ (from MIMI/c Mao/ing on Mt Gum/and lu' Cap} 2 - Lu I son/“opt mr’uuremenl: an pracnnd Mar / 3 — Dar, 5! lH/mm "ism/c "marina an Mr Ron In SIM/f J 4 -- Bear/e; (from nil/nit Mooring /n nu Ania/din / I I I I I 0.4 0,5 0.6 07 0.8 0.9 DEN$TY,g/Cm3 "e 2.28 POISSON'S RATIO FOR DRY SNOW VERSUS DENSITY (after MeIIor from RoethIisberger, 1972) I I I I O 04 05 06 07 08 09 DENSITY~ g/cm3 COMPLEX DYNAMIC POISSON'S RATIO 0 N ?.29 POISSON'S RATIO OF ICE VERSUS DENSITY (after Smith, I969) 64 Boston blue clay NR 1 $5 D- 4 K I” 2 O 0') ‘2 O Q 0 \ TEMPERATURE.°F 0.3vrv1rr III] II IIII IIII _ . A I —1 0 AS I ____, LU? ' 1 A . o A 9 3 , ‘u v V! t; 04 it ~ V 1079 w A (I “K V y )1 , m X )(A A . Z I A If ‘ I o A . ’,,A 3 02 V .-,. ,‘ r_->-_.—_—,:—r“”,‘jjl_r, , r,__.# 5 V.Pvr“""-n’—— p ‘1 0 Q A o a p u a V )1 o I IR IVA II I I I I l._._L_i_l—‘A,—__;A—A'__L—t 5O 20 IO 0 -IO —20 TFMPE FAIURE ,“I Open symbols indicate erxuraT vibraiion and cIosed SymboIs indicate IongitudinaI vibration. 2.30 POISSON'S RATIO OF FROZEN CLAY VERSUS TEMPERA- TURE (after Kaplar, T969) vibration ture. Kap longitudin. able. Inv Poisson's 3 I32 and 0. Stevens inc influenced level . 65 :ion and is apparently not influenced by tempera— Kaplar comments that the values computed using :udinal vibrations are believed to be more reli— In another study conducted by Stevens (1973), >n's ratio of Goodrich clay was found to be between 1nd 0.58 for a temperature range of O to 25°F. IS indicates that Poisson's ratio is apparently not anced by temperature, dynamic stress, and frequency SAI Thi tOrll prepal inStallavtic 0f the tria SamPles. A test SY Stem dI’nélmic pro Adetailed SystemI Spe. test System In recordi] Appendix A. CHAPTER III SAMPLE PREPARATION, SAMPLE INSTALLATION, TRIAXIAL CELL ASSEMBLY, AND TEST PROCEDURE 3.1 General This chapter provides information on the labora— aparation of samples of ice and frozen clay, ition of the samples in a triaxial cell, assembly :riaxial cell and the procedure used to test the A basic understanding of the cyclic triaxial tem used in the research program to evaluate the properties of ice and frozen clay is assumed. ed description of the components of the test Specifically the MTS electrohydraulic closed loop :em, a triaxial cell, a cooling system and out- :ding and monitoring devices, is given in A. 3.2 Preparation of Ice Sample he cylindrical polycrystalline ice samples used search program were prepared using natural snow Lled water for high density samples (about 0.904 Iatural snow and carbonated water for low 66 density sa teflon mol 1.3 cm thi Figure 3.1 follows: (I. 67 y samples (about 0.77 g/cc). Hollow cylindrical molds, 7.1 cm inside diameter, 30.5 cm high and thick were used to form the ice samples (see 3.1). The frozen ice samples were prepared as (l) The mold, with the bottom cap inserted at one end, and the top cap, were placed in a large freezer box maintained at a temperature of - 20 i 1°C. (2 The mold and caps were chilled for approxi— V mately one hour and the mold was filled with loose, dry, clean snow (passing the no. 4 sieve) up to about two inches from the top. (3 Precooled water (close to 0°C) or carbonated V water was poured into the snow from the top and the top cap was inserted. A hole, 0.3 cm, drilled at the side of the mold (5.0 cm from one end), was used to release air which was trapped in the mold during the insertion of the top cap. 4) The sample was placed in the freezer box and left for approximately 24 hours. were then extruded outside the freezer with a hydraulic jack as fast as possible. (It was found that if a sample was left in the mold outside the freezer for approximately The samples Figure 3 ure 3.1. HOLLOW CYLINDRICAL TEFLON MOLD AND SAMPLE CAPS WITH COUPLINGS. e 3.2. TYPICAL CYLINDRICAL ICE SAMPLE. The result and bubbly in Figure 0.908 g/cc to 0.782 9 one out of cracks, or in density LLest were, of ice dens CrI’Stals vj apart and e 3‘. 69 5 minutes or longer tension cracks occurred, presumably due to shrinkage of the samples caused by a temperature increase.) resulting polycrystalline ice samples were cloudy Iubbly in appearance. A typical ice sample is shown gure 3.2. Measured densities ranged from 0.900 to g/cc for the high density samples and from 0.767 782 g/cc for the low density samples. Approximately Jt of two samples contained excessive bubbles, 5, or voids, or appeared to have large variations 1sity and were rejected. The samples used in the Iere, therefore, quite homogenous for the two ranges density. There was a slight radial pattern of ice ls visible in some samples when they were broken and examined in cross—section. 3.3 Preparation of Frozen Clay Sample Two types of frozen clay samples were used in the h program: (1) Ontonagon clay, termed "O-clay," a mixture of Ontonagon and sodium montmorillonite 0 percent each by weight), termed "M+O—clay." The vas prepared at different water contents to assess .uence of water (ice) content on dynamic properties. clay was used to investigate the influence of surface areas (related to unfrozen water con- dynamic properties. The physical properties of both clays previously were thorc content 51 resultant one month samples we (1 lays are given in Table 3.1. 70 The air—dried clays, usly crushed and screened through the no. 40 sieve, oroughly mixed with distilled water to a water slightly greater than their liquid limit. The nt slurry was stored in a humidity room for about th prior to sample preparation. The frozen clay were prepared as follows: (1) The clay slurry was taken from the humidity room and isotropically consolidated in a triaxial cell in a cylindrical shape approxi- mately 10 cm in diameter and 20 cm high. To facilitate drainage, porous stones were placed on the top and bottom of the sample and four vertical paper drainage strips were placed around the sample. Differences in water content of the clay samples were ‘obtained by consolidating the clay slurry in the triaxial cell to different confining pressures. The consolidated sample was taken from the cell and trimmed to a diameter which was slightly smaller than the diameter of the teflon mold. The void space between the caps and the coupling assembly was filled with residual soil from the trimming. Table 3.1. a. O-clay Plasti Liquid Plasti Gradat Clay m SurfaCI b' M+O-cla Plastic Liquid Plastic Clay mi Surface 71 E 3.1. INDEX AND MINERALOGICAL PROPERTIES OF O-CLAY AND M+O—CLAY -clay (after Warder and Andersland, 1971) lastic limit 23.6% iquid limit 60.5% lasticity index 36.9% radation (% finer by wt.) 2 mm 100 0.06 mm 90 0.002 mm 70 .ay mineral content of clay fraction Illite 45% Vermiculite 20% Kaolinite 15% Chlorite 10% Montmorillonite, quartz, feldspar, and amorphous material 10% 2 rface area 215 m /g D—clay iStiC limit 46.3% {uid limit 94.5% isticity index 48 2% .y mineral content of clay fraction Illite 22% Vermiculite 10% Kaolinite 7% Chlorite 5% Montmorillonite, quartz, feldspar, and amorphous material + Sodium Montmor— illonite 56% 2 475 m /g face area determine( the pore I consolida1 that the 5 Saturated, Fc Samp198 we slurrv diz 72 (3) The sample was put in a mold and the two caps were forced into the two ends of the molds with a hydraulic jack. The mold was placed in a freezer maintained at a temperature of -30 i 1°C for approximately 24 hours. The sample was then extruded outside the freezer box with a hydraulic jack. The sample was not subjected to a surcharge load during freezing. The degree of saturation of a few samples was ned after isotropic consolidation by measuring e pressure parameter E. The values of E of the dated samples were greater than 0.98, indicating 2 - samples were, for all practical purposes, fully ad. Four of the highest moisture content O—clay were prepared by pouring the unconsolidated clay Iirectly into the teflon molds. The molds were rated to insure that no air was trapped in the before they were put in the freezer box. The frozen clay samples prepared had a random ion of ice lenses whose thicknesses varied from Jr the lowest water content samples to 2.0 mm lighest. Photographs of typical frozen clay ire shown in Figure 3.3. There was a thin film Irrounding the specimens caused by water being Figure 73 .GVm ENSW” ... —————--r .:—" .T.'. ~ -".":" - .g- . 1re 3.3 TYPICAL CYLINDRICAL FROZEN CLAY SAMPLE expelled Thus, the lower tha: is exempl; was remove ples was < their leng given in '1 TI i 1°C and the Sample of ice len ties, A V to Several was found ”ing the These resu Constraint freezing p; counteract 74 ed from the samples during the freezing process. the water content of the frozen samples was slightly than that of the material placed in the molds. This nplified by the data given in Table 3.2. (The film noved before the water content of the frozen sam- is determined.) The frozen samples were weighed, .engths measured, and their densities obtained, as n Table 3.2. Three samples were frozen at a temperature of -5 nd it was found that they were not different from ples frozen at —30°C in terms of the orientation lenses, water content, and their dynamic proper- I vertical load equivalent to 15 psi was applied 'al samples during the freezing process and it d that these samples were not different (consid- 2 parameters mentioned above) from the others. sults apparently indicate there was significant It between the mold and the sample during the process. The constraint was sufficient to t the frost heave force and the associated at of ice lenses. In an attempt to produce :e lenses, many samples were frozen at —5 i 1°C Irizontal or vertical constraint. It was pos- roduce ice lenses up to 5 mm, however, the uld not be used in the test program because and the caps were not in alignment. A high Table 3. 2 Sample con Number be mmmm 00-30. 3 (j I La.) 0 III-3o. “$30. #WMI—l mm:n(n 75 3.2 WATER CONTENT AND DENSITY OF CLAY SAMPLES Water Average Water Average content water con- content water con- Density : before tent before after tent after of frozen freezing freezing freezing freezing samples (%) (%) (%) (%) (g/CCI 29.8 28.5 1.96 29.9 29.6 1.92 30.3 29'8 29.8 29'2 1.98 29.1 29.0 2.00 39.5 36.8 1.78 38.7 35.5 1.80 38.4 36.1 1.82 37.9 35.3 1.82 38.3 38.6 36.4 36.0 1.82 37.6 34.9 1.81 37.5 34.5 1.86 38.7 36.1 1.84 41.0 38.3 1.82 50.5 50.5 46.3 46.3 1.73 61.0 55.2 1.60 61.0 55.4 1.61 61.0 61°C 54.7 55°l 1.64 61.0 54.9 1.60 58.5 56.4 1.65 57.9 56.9 1.68 61.1 58°8 59.0 57'2 1.59 57.8 56.6 1.70 degree of triaxial TI freezer a‘ rubber Iver Prior to I (see Apper ple base. the base w The anti-t (l (4) 76 of alignment is necessary to perform the cyclic 3 -al tests on the frozen samples. 3.4 Sample Installation and Triaxial Cell Assembly The frozen ice and clay samples were stored in 1°C after they were jacketed with two r at ~20 i each with a wall thickness of 0.05 cm. membranes, to testing, the base clamp of the anti—tilt device >pendix A, Section A.2) was connected to the sam— :e. The sample was immersed in the cold bath and e was connected to the load cell (see Figure A.7). i—tilt device was assembled as follows: (1) The LVDT body was attached to the standard of the anti—tilt device fixed to the base clamp. (2) The anti-tilt ring with the core of the LVDT attached was clamped to the tOp cap. The anti—tilt ring (opposite to the core of the LVDT) was connected to the spring steel extending from the base clamp in a position such that the voltage output from the LVDT was close to zero. The position of the LVDT body was adjusted so that the core of the LVDT was at the center (horizontal plane) of the LVDT housing. This insured that the core would not come into Af sample the Plate 0f t; around the down on the coIInECted 1 bushing 105 ing the Die the pistOn 77 contact with the housing when conducting a test. This adjustment is very important. If any contact between the core and the LVDT occurs, the damping ratio obtained at low strain amplitudes is significantly larger than the correct value. Core contact with the housing could be observed from the hysteresis loops as shown in Figure 3.4. If the line of the loops squared off at the end points it indicated that the load was chang- ing with no change in displacement. However, since the load was changing there must be a corresponding displacement. Therefore, the core must be "sticking" to the housing of the LVDT. The magnitude of this error obviously decreases with increasing strain amplitude. After the anti—tilt device was attached to the e the triaxial cell cylinder was placed on the base of the cell and the thermister collar was placed 1 the sample. Finally, the top plate was tightened In the cell cylinder and the piston loading rod was 'ted to the top cap by inserting it through a ball 9 loading collar. Care must be taken when attach— 3 piston rod. If the torque applied in tightening ston rod is too great the sample will fail. Figure / I DISPLACEMENT line of zero loading ( No scale ) Figure 3. 4 OBSERVED HYSTERESIS LOOP FOR LVDT CORE IN CONTACT WITH HOUSING was used any deforI elastic dc After the 0f the LVI vertical i ing the hy Shown in p a Satisfac the tOp pl Wh bath was c. line Was p. Ismail in< during the SamTies Wei inSure temp samPle befc ture of the ter thermos therTIIStOrS monitOred t. If the temp. 79 Since the LVDT attached to the anti-tilt device : used for the feedback signal to the MTS controller, ' deformations associated with loose connections or stic deformations of the piston rod were eliminated. er the piston rod was attached, the center positioning the LVDT core could be checked by applying a cyclic tical force manually to the connecting rod and observ— the hysteresis loop. If the loop exhibited the shape In in Figure 3.4 the LVDT body had to be reset until Itisfactory loop was obtained. This required removing top plate and piston loading rod. When a satisfactory loop was obtained the cold was covered with styrofoam and an auxiliary coolant was placed on the top plate of the triaxial cell. 111 increase in temperature was usually experienced lg the installation of the sample. Therefore, the .es were left in the cell for at least two hours to e temperature equilibrium in the triaxial cell and e before a dynamic test was conducted. The tempera- Df the sample was controlled by the mercury thermome— Iermostat in the refrigeration unit. The two Lstors attached to the side of the sample were Jred to obtain the temperature to within i 0.1°C. 9 temperature was not correct, the thermostat was ,sted and the test was delayed two hours to insure temperature equilibrium condition was reached. A to apply cyclic tr. research : 80 3.5 Test Procedure An electrohydraulic closed-loop system was used pply a cyclic deviator stress to the samples for ic triaxial testing. The test procedure used in the arch is as follows: (1) The LVDT in the actuator was used as the feed- (2) back signal to move the actuator ram in con— tact with the triaxial cell piston loading rod. (The sample was subjected to a slight load during this operation.) The hydraulic power supply was turned off and a valve at the supply port of the hydraulic manifold of the actuator was closed to prevent fluid movement. The feedback connection was changed from the LVDT in the actuator to the LVDT on the anti— tilt device. The actuator and the piston loading rod were connected, and a confining pressure of approximately 50 psi was applied to the sample to prevent disturbance caused by the movement of the actuator during the application of hydraulic pressure to the actuator. Gain and Rate adjustments were strongly dependent on the strength of the samples and "snugness" of the connection. For practical purposes, they were readjusted whenever the movement of the actuator, (3 v (4) V 81 observed on the strip-Chart recorder, devi- ated from a sine wave. The Cal Factor and the Zero control of the LVDT were readjusted to correspond to the LVDT on the anti-tilt device. Set Point was adjusted to eliminate any difference between the feedback and the command signal. The hydraulic pressure was then applied and the valve at the supply port of the hydraulic manifold was opened. The actuator was now controlled by the LVDT on the anti—tilt device. In general, it was not possible to set the LVDT exactly at its null point. Therefore, there was an initial voltage from the LVDT that would cause the strip—chart and x-y recorder to go "off scale" when they were set at high sensitivity. To achieve a voltage output close to zero the Set Point and the Zero control of XCDRl were gradually adjusted one after the other. During this adjustment the load on the sample was monitored to insure that an excessive load Was not applied. The sensitivities of the recording devices were set for the range of frequencies and voltage outputs anticipated during testing. I l A (6 v 82 The setting for the load cell could be made from experience after testing a number of samples. When the frequency of testing was less than or equal to 0.3 cps, the hysteresis loops were recorded directly on the x-y recorder. For higher frequencies, the hysteresis loops were recorded by playing back the signal stored in the transient recorder. The results from these two tech- niques were compared and they were found to give, for all practical purposes, equal values of damping ratio. The strip—chart recorder monitored peak-to-peak displacement and load signals. From this record the dynamic elastic modulus could be determined. A confining pressure was applied to the cell and the Zero control of XCDRl (feedback) was adjusted to obtain zero load on the sample (with this procedure there was no change in voltage output from the LVDT). The Span con— trol was set to achieve the desired strain and the frequency of the sinusoidal command waveform was selected. The test was then con— ducted by engaging the Run control. CY 0f laborat the densit group the . felt that : prOperties, Effects on teImperature quenCYI anc' CHAPTER IV DYNAMIC PROPERTIES OF ICE UNDER CYCLIC TRIAXIAL LOADING CONDITIONS 4.1 General Cyclic triaxial tests were carried out on two groups laboratory prepared samples<3fice. In the first group I density ranged from 0.900 to 0.908 g/cc; in the second >up the density ranged from 0.767 to 0.782 g/cc. It was .t that several parameters might influence the dynamic >perties of ice. Hence, in addition to density the 'ects on dymamic properties caused by variations in perature, confining pressure, strain amplitude, fre— ncy, and number of cycles of loading were investigated. 4.2 Test History Effects on Dynamic Properties At the onset of the research program it was felt ; the "test history" a sample experienced might influ- the dynamic properties measured. By test history is t (l) the sequence in which the various physical meters considered in the test program (temperature, ining pressure, frequency, strain amplitude, and Br of cycles) were applied to the sample, and (2) the .tude of the parameters considered following a given 83 sequence . establish be summar ( Iuence. 84 The results of the many tests conducted to :ablish an acceptable test history for a sample may summarized as follows: (1) Temperature——individual samples were tested (2 v through a range of temperatures. It was found that the dynamic properties were comparable to those of samples tested at a single tempera— ture if the samples were tested from high (—1°C) to low (—lO°C) temperature. It was observed that if the sample temperature was decreased and it was allowed to readjust to the new temperature for a 24-hour period it would "erase" any disturbance effects that might have occurred at the higher temperature. When the tests were performed from low (-10°C) to high (-l°C) temperature, the samples were disturbed, apparently at the coupling, even if they were left in the cell at a new test temperature for 24 hours prior to testing. The disturbance could be observed from the hysteresis loop. Melting between the samples and the caps was found when the samples were taken out of the cell. Strain amplitude—~the laboratory tests were conducted from low to high strain amplitude at a given confining pressure. If the sample (3) 85 was retested at the lowest strain amplitude it was observed that the damping ratio of the later test was greater than the damping ratio of the former by about 50 percent. The dynamic Young's modulus appeared to be equal in magnitude. Confining pressure——when the samples were subjected to a high confining pressure (greater than 100 psi) they deformed rapidly. The rate of deformation decreased with time and the volume of the samples appeared to decrease which would cause the density to increase. This effect was demonstrated by testing a sample at a low confining pressure, subject— ing it to a high confining pressure, then retesting at the low confining pressure. The dynamic Young's modulus of the sample after it was subjected to a high confining pressure was slightly greater than the dynamic Young's modulus of the sample before experiencing the high confining pressure. To avoid this prob— lem the samples were subjected to the highest confining pressure (200 psi) used in the test sequence for approximately 20 minutes before a test was performed. The rate of deformation of the samples was very small for subsequent the resea] test Condj ditions a: subjected 86 applications of confining pressure after employing this procedure. (4) Frequency--variations in the frequencies of testing (0.3, 1.0, and 5.0 cps) did not appear to cause sample disturbance. (5) Number of cycles--the dynamic properties of the ice samples did not appear to be influ— enced by the number of cycles a sample was subjected to provided the number of cycles of loading did not exceed approximately 20 per one test. One sample was found to be dis- turbed when it was subjected to more than 100 cycles per one test. A sample subjected to about 150 cycles per one test melted at the couplings and the dynamic Young's modulus was found to be very low. An acceptable test history and the one used in the research program is shown in Figure 4.1. The range of I teSt conditions was chosen to correspond to the field con— ditions and loadings anticipated for frozen soil deposits SUbjected to strong motion earthquakes (Vinson, 1975). The range of Specific test parameters are as follows: (1) Temperature—-the high density samples were tested at five temperatures (-1, -2, -4, -6 and —10°C); the low density samples were tested at three temperatures (-l, ‘4 and Constant t (sample su prior to t :p' L 4 IT: "U E I" O FFFI' 4* V A r0) ‘7‘7’7—1—7‘3 87 Constant temperature (sample subjected to an initial confining pressure of 200 psi prior to testing) 3 Approximate axial strain = 3 x 10_ % cp=200 psi-—-v-f=0.3 cps—>f=l.0 —-o-cp=100 psi—>f=0.3 cps—>f=1.0 L—o-cp= 50 psi—»f=0.3 cps—>f=l.0 L_.cp= L_.Cp= I ApFroximate axial strain = L‘cp=200 psi—*f=0. 3 cps —"f =1. 0 25 pst=0.3 cps—>f=1.0 0 psi—>f=0.3 cps—+f =l.0 9 x 10'° '—o-cp=1oo psi——.-‘F=O.3 cps-—hf =1.0 [—O-cp= 50 psi——O-f=0.3 cps—+1: =l.0 y—bcp= 25 psi—>f=0.3 cps——-f =l-0 I 2 Approximate axial strain = 2 x 10- I p=200 psi—>f=0.3 cps—>f=l-0 ’ "CP=100 pSi—*f=0.3 cps—bf =1.0 Figure 4.] cps—o- 1‘ =5.0 cps—+1” =5.0 cps—pf =5.0 cps—pf =5.0 cps—pf =5 . 0 cps-""1c =5.0 cps—pf =5.0 cps——o-f =5.0 (:pr =5 . 0 CPS—.1: =5. O (3pr =5. 0 DIAGRAM OF ACCEPTABLE TEST HISTORY FOR ICE cps cps cps cps cps cps cps cps cps cps cps (2) (3) 88 —10°C). A given sample was tested at one temperature only. Strain amplitude——the range of strain ampli- 3 to 2 x 10‘2% tude was approximately 3 X 10- axial strain. The maximum strain amplitude of testing at cp = 0 was limited to about 5 X 10_3%; at cp = 25 and 50 psi it was limi— ted to about 9 x 10'3e; at Cp = 100 and 200 psi it was limited to about 2 X 10—2%. The maximum strain amplitudes were associated (approximately) with a tensile failure of the sample. (It was found that ice samples with the coupling described in Appendix B could be subjected to a tensile stress of about 80 psi.) Confining pressure-—the high density samples were tested at five confining pressures (0, 25, 50, 100 and 200 psi). At a confining pressure of 0 psi, only a limited number of tests were performed at low strain amplitudes 3 to 5 x 10‘3 (2 x 10' %). The low density samples were tested at four confining pres— sures (0, 25, 50, and 100 psi). The low density samples were not tested at cp = 200 psi because the deformations associated with the application of this confining preSSure 89 were quite large. (The deformation of the low density samples under 200 psi confining pressure was greater than the range of the LVDT, t 0.254 cm.) At a temperature equal to —1°C, the maximum confining pressure was limi- ted to 50 psi, because of excessive deforma- tions at 100 psi. A limited number of tests were performed at cp = 0 psi at low strain 3 39 O. amplitude, 3 x 10‘ and 5 x 10' (4) Frequency-—in general only three frequencies of loading were used in the test program: 0.3, 1.0 and 5.0 cps. A limited number of samples were tested at a very low frequency, 0.05 cps. (5) Number of cycles—-for each test condition a sample was subjected to 20 cycles of loading. Before a sample was subjected to the acceptable test history the cell pressure was increased to 200 psi for approximately 20 minutes. The dynamic Young's modulus was evaluated at a strain amplitude of 9 x 10-3% and a frequency of 0.3 cps. The value obtained from this test was compared to that obtained during the course of the test history as another check on the disturbance of the sample. If they were found to be in good agreement, the test was presumed to be acceptable. (For all the test results reported herein the comparison was quite good.) I1 cyclic tri properties most apprc earthquake cYcle numb ratio (E a cYCle/I at freilllencie: te'“IIEraturg high densit and ”I re Variation 1 for differe amTlitudes, dlnamc You W differ. ther, the c' the nufllber < pressures I II ampint ratj Iereut frOm The be kind and 90 4.3 Influence of Number of Cycles on Evaluation of Dynamic Properties It is generally felt by researchers conducting cyclic triaxial tests on unfrozen soils that the dynamic properties associated with the 5th or 10th cycle are the most appropriate for predicting ground response during earthquakes. To assess the influence of the choice of the cycle number on dynamic properties the variation of the ratio (E at Nth cycle/E at 10th cycle) and (A at Nth cycle/A at 10th cycle) with number of cycles at different frequencies, confining pressures, strain amplitudes, and temperature was determined. These ratios are shown for high density ice at l, 5, 10 and 20 cycles in Tables 4.1 and 4.2, respectively. There appears to be no significant variation in dynamic Young's modulus with number of cycles for different frequencies, confining pressures, strain amplitudes, and temperatures. At the greatest, the dynamic Young's modulus at the Nth cycle is approximately 3.0% different from the modulus at the 10th cycle. Fur- ther, the damping' ratio does not appear to vary with the number of cycles for different frequencies, confining pressures, strain amplitudes, and temperatures. The damping ratio at the Nth cycle is at most about 10% dif— ferent from the damping ratio at the 10th cycle. The dynamic Young's modulus was evaluated from the load and displacement channels of the strip-chart IrIII (FIZZ 44 u .I l lullII riwxrn WMHAHHUMWU mo mmszz 39H: MHUH Mfln—vazummo THMVHHH nHO WDJHDQOZ W.UZDON UHEANZLHQ 0H0 ZOHUANHNNANKV HIV ”HORNE mHo.H H HHo.H «mo.H m.o om ammoo.o oHI «Ho.H H mHo.H mam.o m.o om ammoo.o «I mHo.H H moo.H coo.H m.o om smmoo.o HI «mm.o H mam.o omm.o m.o oom NmHo.o «I moo.H H moo.H moo.H m.o com mmoo.o «I «Ho.H H mHo.H Nam.o m.c com ewmoo.o «I moo.H H mmo.H mHo.H m.o com emHoo.o «I smm.o H Hoo.H mmo.H m.o o nmmco.o «I omo.H H «Ho.H mmo.H m.o om emmoo.o «I u mHo.H H «Ho.H Nam.o m.o com smmoo.o «I mmm.o H moo.H Noo.H o.m om emmoo.o «I «No.H H NHo.H Hmm.o o.H om ammoo.o «I omo.H H «Ho.H mmo.H m.o om ammoo.o «I mam.o H moo.H wmm.o mo.o om swmoc.o «I om mH m H a w 0 U O MN m on H u 852 ass 3 c i c 6.; mucosooum whommoum oUDuHHmEm ousflfiomfima mHumo auOH um m mchHuaoo :Hanpw Hmem mHoNo suz um,m mmAUMU .mO MMMZDZ EBHE WUH wBHmZWQ mOHm .mO mDADQOE m.OZDOM. 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UNIQMPU w«o.H H ooo.H moH.H m.o om hmmoo.o CHI «mm.o H mmo.H mmo.H m.o om hmmoo.o «I moo.H H nhm.o mmm.o m.o om nwmoo.o HI H H HNo.H wam.o m.o com . mmHo.o «I MHo.H H mom.o mnm.o m.o oom mmoo.o «I noo.H H wmm.o ««m.o m.o oom nmmoo.o «I N«m.o H mom.o omm.o m.o oom hmHoo.o «I onm.o H mom.o onm.o m.o o . smmoo.o «I «mm.o H mmo.H mmo.H m.o om nmmoo.o «I hoo.H H mmm.o ««m.o m.o com nmmoo.o «I 2 «mm.o H mmo.H mmo.H m.o om nmmoo.o «I 9 Hem.o H owm.o mom.o mo.o om nmmoo.o «I om OH m H oHowo mo Hooeoz Ammov AHmmv Hwy AU v mocosoou whommoum opsuHHmEm mus mummfio oHomo QuOH box m mcHnHmcoo chnum Honm # B oHoNo npz uma mMQOMU .mO mmmEDZ EBHB HUH NBHmZMQ mUHm .mO OHBHMNH OZHAHSANQ inHO ZOHBflHmflxw N.w mHQwB recorder amplitud was eval obtained X-y recor of the h) The error ted to be test prOg. amIllitucie i“ Append; Samples ar SamPles. ated with pressure, are avails F0: in the date (1) 93 recorder at the 10th cycle by measuring the peak—to—peak amplitude of the recorded waveform. The damping ratio was evaluated from the hysteresis loop for the 10th cycle obtained from the x—y recorder. Typical strip chart and x—y recorder records are shown in Figure 4.2. The area of the hysteresis loop was determined with a planimeter. The error associated with this determination was estima— ted to be approximately 5%. 4.4 Dynamic Young's Modulus of Ice The dynamic Young's modulus from the laboratory test prOgram was plotted against the log of axial strain amplitude expressed as a percent. The plots are shown in Appendix C, Figures C.l to C.93 for the high density samples and Figures C.94 to c.126 for the low density samples. Each plot represents a test condition associ— ated with a specific frequency, temperature, and confining Pressure. In general, the data from three (or more) tests are available for each test condition. For any given test condition there is "scatter" in the data points. It is believed that this was caused by: (l) Slight variations of density of the samples which ranged from 0.900 to 0.908 g/cc for the high density samples and 0.767 to 0.782 g/cc for the low density samples. \ \\§ A °Dfi\°~ 0A0» \AUEOJUOLk 94 muH do wzHmeH 4o oszzo omzHH N.« wrsmwd ,mutooog ucmswomHQmwu oco.omoH Hmowaze .n \/ \/ \/ \/M \ / \ / \ / \ o i / i / i / i \ < < < / > > > / \ / \ / \ / . : : : i /<\ /r\\ /C\ /r\ mooo. (90) P001 ('ug) Iuauiaomdsgg n. AHmcovmcoEoncocv maooH memogopmxc Hmowaae no. 3383?: accesses... .m 95 (2) Slight differences in the structural compo- sition of the samples, particularly near the coupling. (3) Slight temperature differences between tests. (4) Loosening of the coupling between the samples and the cap and base. (5) At the lower strain amplitudes of testing the test system approached its limit of capa- bility both electronically and mechanically. Some variations in test results at this extreme of testing are to be expected. Overall, however, it is felt that the data is reliable and provides a good basis for the interpretation of material properties. 4.4.1 Effect of Strain W The data presented in Figures C.l to C.126 in Appendix C suggests that the dynamic Young's modulus of ice varies linearly with the log of percent axial strain amplitude, at least over the range of strain amplitude associated with the experimental program. The dashed lines in the figures represent the least squares best fit line Of the data. The slopes of the least squares best fit lines vary slightly from one another but do not appear to be influenced by frequency, confining pressure, or temperature. The slopes of a few of the lines vary g signifies they are points. C.4l, C.6 and at a S. modulus a1 nificantl3 assumed tc the averag Young 'S me against 10 in Figure for the 10‘ (psi/log %; 109 %) for indicate tr. high densit Samples. To and Confini; image bes‘ data points issolid lir drawn inters 319 data 361; 96 significantly from the majority of the lines because they are associated with only a limited number of data points. This is exemplified by Figures C.l, C.16, C.21, C.4l, C.6l, C.66 and C.77 at a confining pressure of 0 psi and at a frequency of 0.05 cps. Since the relationship between dynamic Young's modulus and the log of percent axial strain is not sig- nificantly influenced by other test parameters it was assumed to be independent of the parameters. To establish the average least squares best fit line the dynamic Young's modulus for all the experimental data was plotted against log of percent axial strain amplitude, as shown in Figure 4.3 for the high density samples, and Figure 4.4 for the low density samples. The average slope is —0.0934 (psi/log %) for the high density samples and 0.0067 (psi/ 109 %) for the low density samples. The average slopes indicate that the influence of strain amplitude for the high density samples is greater than for the low density samples. To assess the influence of frequency, temperature, and confining pressure on the dynamic Young's modulus the average best fit least squares line was plotted through the data points for a given test condition. These are shown as Solid lines in Figures C.l to C.126. These lines were drawn intersecting the dashed lines at the "center" of the data set for a given test condition. Obviously, L 97 Sample density = 0 904 g/cc 900. A439. . s 800. ’A‘“ ,-.\ A :fi». A“,€;‘. AAA}; ,‘ /? .5700. AMS'f Q A‘ :_x 0‘) O m600. 3 3 £3 '0 O Z [3 U) 12.500. A A 3 2 fl .2 [5 E400. a D 300. L- 200. " 100. J l l L I -3.00 —2.68 —2.36 -2.04 -1.72 Axial Strain (Tog percent) Figure 4.3 LEAST SQUARES BEST FIT LINE FOR DYNAMIC YOUNG'S MODULUS OF HIGH DENSITY ICE VERSUS AXIAL STRAIN 900. 800. 'I 900. 800. 700. . Dynamic Young's Modulus (103 psi) 300. 200. lOO.‘ 600. 500. 400. 98 Sample density = 0.77 g/cc l> D>fi DB '>’ % gm $.33 A SA Mes AAA A e. i? Ase as AAAAA AA .3 8A./\ A 1% AA % AA A AA A A g. A A A :93 A A: A if A A A A A l l J l -3.08 -2.76 -2.44 -2.l2 Axial Strain (log percent) Figure 4.4 LEAST SQUARES BEST FIT LINE FOR DYNAMIC LON DENSITY ICE VERSUS AXIAL STRAIN YOUNG'S MODULUS 0F personal best fit data set Figures 1 Figures 1 figures 5 dynamic Y frequency to 900 x 260 x 103 TL and ConfiT EStablism Pi(lures 4. mis Chapt 1'36) was amplitude 99 personal judgment was involved in this construction. The best fit least squares line through the center of the data set for given test conditions are summarized in Figures 4.5 to 4.23 for the high density samples and Figures 4.24 to 4.32 for the low density samples. The figures show the influence of confining pressure on dynamic Young's modulus at a specified temperature and frequency. Dynamic Young's modulus varies from 340 X 103 to 900 x 103 3 to 600 X 103 psi for the low density samples. psi for the high density samples and 260 X 10 The relationship between dynamic Young's modulus and confining pressure, frequency, and temperature can be established by interpolation of the results presented in Figures 4.5 to 4.32 at a specified strain amplitude. In this chapter a strain amplitude of 4.4 X 10_3% (loglo = -2.36) was selected for this purpose. Another strain amplitude could be selected without changing the conclu— sions reached in Sections 4.4.2, 4.4.3, and 4.4.4 owing to the fact that the variation between dynamic Young's modulus and log percent axial strain was assumed to be linear and independent of confining pressure, frequency, and temperature. 4.4.2 Effect of Confining Pressure The relationship between dynamic Young's modulus and confining pressure at an axial strain of 4.4 x 10-3% 980. ' 900. ' 820. ' 580. " ~ 0" 0 5 420. r 340. " 260. ~ Flgm Dynamic Young's Modulus (103 psi) 980. 900. 820. 740. 660. 580. 500. 420. 340. 260. 100 Sample density = 0.904 g/cc cp = 200 psi CD = 100 psi cp = 50 psi CD = 25 psi l l l I -3.00 -2.68 -2.36 -2.04 —l,72 Axial Strain (log percent) Figure 4.5 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT -I°C AND 0.05 CPS 980. "' 900. " 820' _ 740. " A F ”HQ 660. " 580. T Am.» I ‘wulin J I“ V 0 Ar: 500. ‘ 420. " 340. ~ 260. ~ FIQUI‘I Dynamic Young's Modulus (103 psi) 980. 900. 820. 740. 660. 580. 500. 420. 340. 260. 101 lu— Sample density = 0.904 g/cc *- cp = 200 psi CD = lOO psi *- CD = 50 psi CD = 25 psi m L—n l I l ' l l -3.00 -2.68 -2.36 -2.04 -1_72 Axial Strain (log percent) Figure 4.6 DYNAMIC YOUNG‘S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT —I°C AND 0.3 CPS 980. " 900. "' 820. h - nU. 4 I’ll “pun. ~ c 8 5 660. ‘ W3 3°02 W 0:10) U .mHo -. v 500. .. hldF§\Alfi.N 340, ~ Dynamic Young's Modulus (l03 psi) 980. 900. 820. 740. 660. 580. 500. 420. 340. 260. 102 Sample density = 0.904 g/cc cp = 200 psi _ CD = lOO pSi CD = 50 psi CD = 25 psi m __J_____, l l l l ‘3.00 -2.68 -2.36 -2.04 -I.72 Axial Strain (log percent) Figure 4.7 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT -I°C AND 1.0 CPS 980. - 900. ' 820. " 740. ' Am m0. 660. " 580. '- U x) 13 m: m‘ no: - J J m g v mo 500. - 420. ~ 340. -. Dynamic Young's Modulus (l03 psi) Sample density 2 0.904 g/cc CD = 200 psi CD = 100 psi CD = 50 psi CP= 25 psi 1 l I -3.00 -2.68 —2.36 -2 04 -l 72 Axial Strain (log percent) Figure 4.8 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT -I°C AND 5.0 CPS 980. 900. 82-0. - 0 on? 7 ArWQ 660. '- 580. - MIOFV WINS-U0: MamL‘uo) U h DU. 0 5 UDMXIQ 420. . 340. ~ 260, . FiSim Dynamic Young's Modulus (103 psi) 900. 820. 740. 580. 500. 420. 340. 260. 104 Sample density : 0.904 g/cc CD = 200 psi CD = lOO psi CD = 50 psi cp = 25 psi l l l I -3-00 —2.68 -2.36 -2.04 -l.72 Axial Strain (log percent) Figure 4.9 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT -2°C AND 0.05 CPS 980. 900.. 820. 740. - A? MD. 660. " 580. " HIV 3) all. A“ a). , ‘dno 4.]: V L- no 500. " 420. ‘- 340. ‘ 260. " Figu Dynamic Young's Modulus (l03 psi) 105 Sample density = 0.904 g/cc CD = 200 psi CD = lOO pST CD = 50 psi cp = 25 psi m J l l I -3 00 —2.68 —2.36 -2.04 —l 72 Axial Strain (log percent) Figure 4.10 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT -2°C AND 0.3 CPS 980. ' 900. ' 820. " 420. ~ 340. . 260. 5 ~ “v. 0 5 580. ~ 00 00 a 6 7 6 3:83 ATWQ Milo-iv WJHJ—UOE W.m:30\r “VT-I: Dynamic Young's Modulus (l03 psi) 106 Sample density = 0.904 g/cc CD = 200 psi cp = lOO psi cp = 50 psi CD = 25 psi cp = 0 psi 1 l l l -3 00 -2.68 -2.36 -2.04 -l.72 Axial Strain (log percent) Figure 4.11 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT -2°C AND I.0 CPS 980. 900. 820. ' 740. ' Ilyl 660. - 580. " J \» ‘.UA. \J 30: .4 I ‘.- A: V o u m 1“ unflhlix I 420, '- 340. .. Dynamic Young's Modulus (l03 psi) 107 Sample density = 0.904 g/cc CD = 200 psi C = lOO psi CP = 50 psi CD = 25 psi 1 l I I -3.00 -2.68 -2.36 -2.04 -l.72 Axial Strain (log percent) Figure 4.12 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT -2°C AND 5.0 CPS 980. 900. 820. 0 4 7 awWQ 0 0 0 Milo—iv WJPJUOPQ W. Dav—L30} U?~..CH~C\ATQ 420‘ . 340. - 260_ . Dynamic Young's Modulus (103 psi) 980. 900. 820. 740. 660. 580. 500. 420. 340. 260. 108 Sample density = 0.904 g/cc cp = 200 pSi CD = 100 psi \Cpflopg cp = 25 psi w l l l l ~3.00 -2.68 -2.36 -2.04 —1.72 Axial Strain (log percent) Figure 4.13 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT —4°C AND 0.05 CPS 980. 900. 820. 0 4 7: A? mu 6 5 o U- Ohv WJHJUOZ H.0E3 > Mm 500. .. h. hh§fiiEXIHiN 420. .. 340. a 260. . Fig Sample density = 0.904 g/cc CD = 200 psi CD = 100 psi '5 D. 0 E3 CD = 50 psi U) 3 3 U 2 CD = 25 psi In 9 CP= 0 psi 5 3 3 5 l I l 1 —3.00 —2.68 —2.36 —2.04 -l 72 Axial Strain (log percent) Figure 4.14 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT -4°C AND 0.3 CPS 980. 900. 820. 740. A... W0. 0 6 6 HOPV WJP‘JUOE 0 8 5 RI IVI 500. 1' 0:30) Um.:sHI-L\AIQ 340. - 260. . uynamic roung's Modulus (l0° psi) 980. 900. 820; 740. 660. 580. 500. 420. 340. 260. Sample density = 0.904 g/cc _' CD = 200 psi CD = 100 psi CP = 50 psi CD = 25 psi CP = 0 psi _L l l L I -3.00 —2.68 —2.36 -2.04 -l.72 Axial Strain (log percent) Figure 4.15 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT -4°C AND 1.0 CPS 980. 900. 820. 0 1...... A? mn- - 0U 0 . 3 0 .83 6 TEXIHTN JUGS W. J. 30> 0.1.1 Alwi‘dh. DOPV 420. ~ 340, . 280. ~ Fi PJ'I 4—— ‘.v 980. 900. 820. 740. 660. 580. 500. 420. 340. 280. 111 L- Sample density = 0.904 g/cc CD = 200 psi cp = lOO psi - CD = 50 psi " Cp = 25 psi CD = 0 psi __l___, l I I I -3.08 —2.68 -2.36 -2.04 -1.72 Axial Strain (log percent) Figure 4.16 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT -4°C AND 5.0 CPS NFWQ Milo—iv wanna—U02 W-mc‘dnvxr Um.:-N:\AIQ pas; .._——-uu ‘IU Sample density = 0.904 g/cc CP = 200 psi 1 l l l I -3.00 -2.68 —2.36 -2.04 -l.72 Axial Strain (log percent) Figure 4.17 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT -6°C AND 0.3 CPS APWQ MHOFV WJPJUOE W.m:3°> UTEMEXIQ Dynamic Young's Modulus (103 psi) 980. 900. 820. 740. 660. 580. 500. 420. 340. 260. 113 L. Sample density 2 0.904 g/cc cp = 200 psi C = 100 pSl cp = 50 psi _ cp = 25 psi — V I I _I¥ I I -3.00 -2.68 -2.36 -2.04 -l.72 Axial Strain (log percent) Figure 4.18 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT —6°C AND 1.0 CPS 98 90 82l ( 4 7 E 0 0 AFMQ MUOPV Win-.330: Mum-L30) UFENEMQ 0 2 4 340. 260. uynamic voung's Modulus (l0° psi) 980. 900. 820. 740. 660. 580. 500. 420. 340. 260. 114 _l_ l I 1 -3-00 -2.68 -2.36 -2.04 Axial Strain (log percent) Figure 4.19 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL DENSITY ICE AT -6°C AND 5.0 CPS i. » Sample density = 0.904 g/cc CD = 200 psi = 100 pSl M _ cp = 25 psi 1 -1.72 STRAIN FOR HIGH u I E Pk! 5 4 3i 2 AFMQ WOPV WJPJHVOE M.UCJ°> UhENCkiQ Dynamic Young's Modulus (103 PSI) 980. L- 820. " Sample density = 0.904 g/cc cp = 200 psi cp = l00 psi CD = 50 psi 580. I CD = 25 p51 420. -— 340. - 250. - g I I I I -3 00 —2.68 -2.36 -2.04 -l.72 Axial Strain (log percent) Figure 4.20 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT —10°C AND 0.05 CPS I I I \ III AFWQ MOFV WIN—1:00: W.QC30> UmEfivtxfiQ 980. 900. 820. 740. 660. 580. 500. I— ___L__, -3.00 Figure 4.2l 116 Sample density = 0.904 g/cc C = 50 psi P = 200 psi C = lOO pSl \W m I I I I -2.68 -2.36 -2.04 —1.72 Axial Strain (log percent) DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT —10°C AND 0.3 CPS AVWQ WOFV WJFJUOZ W.QCDO> UmEMCXQ 117 Sample density = 0.904 g/cc cp = 50 psi N C p = 0 psi I I I I -3 00 -2.68 -2.36 -2 04 -l.72 Axial Strain (log percent) Figure 4.22 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT —10°C AND 1.0 CPS APW OPV WJF Q 3 Mn “02 W.m:3°> UNI-Nana 980. 900. 820. 740. 380. 30. O. 118 L- Sample density = 0.904 g/cc CD = 200 psi CD = lOO psi CP = 50 psi ._ Cp=25psi . — N I __ I _I_ I 1 l I -3.00 —2.68 -2.36 -2.04 -1.72 Axial Strain (log percent) F1.gur‘e 4.23 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT -10°C AND 5.0 CPS ..WQ MOFV WJPDUOZ W.m23°> UPENCMQ $80. 20. 119 SamPIE density = 0.77 g/cc .. CD = 50 psi CD = 25 psi __ cp = 0 psi I I I I -3-40 -3.08 —2.76 -2.44 -2.12 Axial Strain (log percent) Figure 4.24 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR LOW DENSITY ICE AT ~1°C AND 0.3 CPS _ .. . s. ‘44P" K I~I\I..(> (.III III 740. 660. 300. :5 o 40. 120 Sample density : 0,77 g/cc CD = 50 psi _. CD = 25 psi CD = 0 psi I I I I -3.40 ~3.08 -2.76 -2.44 -2.l2 Axial Strain (log percent) Figure 4.25 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR LOW DENSITY ICE AT -1°C AND 1.0 CPS awMQ NOFV WJFJUOE 0:39.30} UhENCxfiQ 121 Sample density = 0.77 g/cc cp = 50 psi CD = 25 psi cp = 0 psi I I l I -3.40 —3 08 -2.76 -2 44 —2.l2 Axial Strain (log percent) Figure 4.26 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR LOW DENSITY ICE AT -1°C AND 5.0 CPS A .P WQ MOP V W: F‘s-U02 W . m-LJo} vaiuflvpkxiQ 740. 660. 580. 500. 420. 340. 260. 180. 122 Sample density 2 o_77 g/cc _ CD = 100 psi CD = 50 psi CD = 25 psi CD = 0 psi _ I I I I -3.40 —3.08 -2.76 -2 44 -2.12 Axial Strain (log percent) Figure 4.27 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR LOW DENSITY ICE AT -4°C AND 0.3 CPS 7i E 5 A ...WQ MITOPV W‘JFJ—Uoz M. WES-Ox» UfisN-kxiq 18( 10C )0. —3.40 Figure 4.28 123 Sample density = 0.77 g/cc = 100 psi = 50 psi = 25 psi CD = 0 psi l I l l —3.08 -2.76 -2.44 -2.12 Axial Strain (109 percent) DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR LOW DENSITY ICE AT -4°C AND 1.0 CPS APWQ MYOFV WINS-DOV... M.nw-L3°\r UmLiNCXIQ 740. 660. 580. 500. 420. 340. 260. 180. 100. 124 — Sample density = 0,77 g/cc CD = 100 psi — cp = 50 psi CD = 25 psi _ CD = 0 psi F I I I 1 -3.40 -3.08 —2.76 -2.44 -2.12 Axial Strain (log percent) Figure 4.29 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR LOW DENSITY ICE AT —4°C AND 5.0 CPS firMQ WOnv WJHJUQ—L W.DCJO> UpENCXNu 30. IO. 125 Sample density = 0.77 g/cc " CD = lOO psi CD = 50 psi CD = 25 psi CD = 0 psi p— I I l 1111, -3.40 -3.08 -2.76 -2.44 -2.12 Axial Strain (log percent) Figure 4.30 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR LOW DENSITY ICE AT -10°C AND 0.3 CPS 126 Sample density = 0.77 g/cc cp = 100 psi cp = 50 psi cp = 25 psi CD = 0 psi 1 I I I -3.40 —3.08 —2.76 —2.44 -2.l2 Axial Strain (log percent) DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR LOW Figure 4.31 DENSITY ICE AT —10°C AND 1.0 CPS 127 Sample density = 0.77 g/cc I I Al I -3.40 —3.08 —2.76 -2.44 -2.12 Axial Strain (log percent) Figure 4.32 DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR LOW DENSITY ICE AT -10°C AND 5.0 CPS 128 shown in Figures 4.33 to 4.37 for the high density ice Figures 4.38 to 4.40 for the low density ice. The ationship is, in general, plotted at four frequenciEs a given temperature. The data at five temperatures , -2, —4, -6, and —lO°C) was available for the high sity ice, and at three temperatures (—1, —4, and ‘C) for the low density ice. The results shown in Figures 4.33 to 4.37 indicate dynamic Young's modulus of high density ice increases increasing confining pressure (1) gradually from 0 to 5i (approximately 8%), (2) steeply from 25 psi to 50 {approximately 20%), (3) gradually from 50 psi to 100 'approximately 8%), and only slightly from 100 psi to si. Temperature and frequency do not appear to have nificant influence on the relationship between ic Young's modulus and confining pressure. The dynamic Young's modulus of low density ice at :atures of —l and -4°C increases rapidly with Ising confining pressure from 0 to 25 psi (approxi- l4%). At a temperature of —lO°C, the rate of se in this range of confining pressure is gradual mparable to high density ice. The dynamic Young's 3 increases gradually for all test temperatures Icreasing confining pressure from 25 psi to 50 psi; Ilmost constant with increasing confining pressure psi to 100 psi. Frequency does not appear to have 900. 129 Frequency Sample density = 0.904 g/cc ‘3 0‘05 CPS Axial strain = 4.4x10'3% 45 0.3 cps It l.0 cps ‘A. 5.0 cps . l A s I J I I I I 11 I 25 50 75 100 125 150 175 200 Confining Pressure (psi) Figure 4.33 DYNAMIC YOUNG'S MODULUS VERSUS CONFINING PRESSURE FOR HIGH DENSITY ICE AT -1°C 130 30, Frequency Sample density = 0.904 g/cc ‘5 0'05 cps Axial strain = 4.4x10_3% A; 0.3 cps 3. ll l.0 cps “‘5.0 cps I L. l I l L I J 25 5O 75 100 125 150 175 200 Confining Pressure (psi) Figure 4.34 DYNAMIC YOUNG'S MODULUS VERSUS CONFINING PRESSURE FOR HIGH DENSITY ICE AT -2°C 900. 131 Frequency Sample density = 0.904 g/cc l - A 0-05 CPS Axial strain = 4.4xio‘3z AIO.3 cps 13 1.0 cps ' A 5.0 CPS I I I J J, I l I 25 50 75 100 125 150 175 200 Confining Pressure (psi) Figure 4.35 DYNAMIC YOUNG'S MODULUS VERSUS CONFINING PRESSURE FOR HIGH DENSITY ICE AT —4°C 900. 820. 560. Frequency Sample density = 0 904 g/cc — A 0-3 CPS Axial strain = 4.4xio'3% (L 1.0 cps A; 5.0 cps I I I I I l I I 25 50 75 100 125 150 175 200 Confining Pressure (psi) Figure 4.36 DYNAMIC YOUNG'S MODULUS VERSUS CONFINING PRESSURE FOR HIGH DENSITY ICE AT -6°C 820. 740. 660. Frequency Sample density = 0.904 g/cc 20. A 0.05 cps Axial strain = 4.4x10‘3z 45 0.3 cps IA 1.0 cps O ‘A,5.0 cps I l I I I I I 25 50 75 100 125 150 175 200 Confining Pressure (psi) Figure 4.37 DYNAMIC YOUNG'S MODULUS VERSUS CONFINING PRESSURE FOR HIGH DENSITY ICE AT -10°C 740. S80. 20. 134 Frequency 15» 0.3 cps II 1.0 cps Al.5.0 cps I I I J 25 5O 75 100 Sample density = 0.77 g/cc Axial strain = 4.4xio'3z I I I I 125 150 175 200 Confining Pressure (psi) Figure 4.38 DYNAMIC YOUNG'S MODULUS VERSUS CONFINING PRESSURE FOR LOW DENSITY ICE AT -1°C h 380. - 00. '- 135 Frequency Sample density = 0.77 g/cc ‘5 0'3 CPS Axial strain = 4.4xlO'3Z ll l.O cps ‘fii5.0 cps I I I I I I I 50 75 100 125 150 175 200 Confining Pressure (psi) Figure 4.39 DYNAMIC YOUNG'S MODULUS VERSUS CONFINING PRESSURE FOR LOW DENSITY ICE AT —4°C 740. — 80. '- 50 136 Frequency Sample density = 0.77 g/cc A 0.3 cps Axial strain = 4.4xio'3% 21 l.O cps Al 5.0 cps I J l I I I 75 100 125 150 175 200 Confining Pressure (psi) Figure 4.40 DYNAMIC YOUNG'S MODULUS VERSUS CONFINING PRESSURE FOR LOW DENSITY ICE AT ~10°C 137 influence on the relationship between dynamic Young's iulus and confining pressure. The relationship between dynamic Young's modulus ice and confining pressure might be caused by changes the microstructure of the ice under various confining :ssures. Microfissures might close when a sample is jected to a high confining pressure. This would lead a sample with a higher dynamic modulus. Conversely, y might open when a sample is subjected to a lower con- ing pressure which would lead to a lower dynamic modu- This tendency was exemplified by the fact that when confining pressure was released from the triaxial L and the sample was not allowed to deform there was a Iual increase of load on the sample. This load might Lssociated with the elastic rebound characteristics of microfissures. 3 Effect of Frequency The relationship between dynamic Young's modulus frequency at an axial strain of 4.4 X 10-3% is shown igures 4.41 to 4.45 for high density ice and Figures to 4.48 for low density ice. The relationship is, eneral, plotted at five confining pressures for a I temperature. The dynamic Young's modulus of high density ice ases rapidly (approximately 20%) for an increase in 138 Confining pressure Sample density = 0.904 g/cc [— A 0 P51 Axial strain = 4.4xio'3% 15 25 psi 15 50 p51 (I 100 pSl " A 200 pSl I I 1 l o 05 0.3 l 0 5 0 Frequency (cps) gure 4.41 DYNAMIC YOUNG’S MODULUS VERSUS FREQUENCY FOR HIGH DENSITY ICE AT —1°C 139 Confining pressure Sample density = 0.904 g/cc L_ 13 0 P51 Axial strain = 4.4x10-3% 15 25 psi A; 50 psi [L 100 psi A 200 psi N I I I I 0.05 0.3 1.0 5.0 Frequency (cps) igure 4.42 DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR HIGH DENSITY ICE AT -2°C 140 Confining pressure Sample density = 0.904 g/cc L. 25 0 p51 3 Axial strai = . 7 18 25 p51 n 4 4x10 % £8 50 p51 _ — — _ 0.05 0.3 1.0 5.0 Frequency (cps) igure 4.43 DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR HIGH DENSITY ICE AT -4°C 141 Confining pressure Sample density = 0.904 g/cc A 25 psi Axial strain = 4.4xio‘3% A: 50 psi 11 lOO psi A 200 psi I I I I 0.05 0.3 1.0 5.0 Frequency (cps) gure 4.44 DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR HIGH DENSITY ICE AT -6°C 142 Confining pressure Sample density = 0.904 g/cc A 0 psi Axial strain = 4.4xio'3% I I I I 0.05 0.3 1.0 5.0 Frequency (CPS) ure 4.45 DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR HIGH DENSITY ICE AT -10°C 143 Confining Pressure Sample density = 0.77 g/cc A 0 p51 Axial strain = 4.4xio'3% 13 25 psi ‘g; 50 psi I l I ' 0.05 0.3 1.0 5-0 Frequency (cps) 'gure 4.46 DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR LOW DENSITY ICE AT -1°C Frequency (cps) lure 4.47 DYNAMIC YOUNG‘S MODULUS VERSUS FREQUENCY FOR LOW DENSITY ICE AT -4°C 144 ‘Confining pressure Sample density = 0.77 g/cc A 0 ps‘ Axial strain = 4.4xio'3% A 25 psi A 50 psi (1100 psi E I I L I 0.05 0.3 l.O 5,0 145 Confining pressure SampTe density = 0.77 g/cc A 0 psi Axial strain — 4.4xio‘3z ’- A 25 psi AL 50 psi Al TOO psi 41 l 0.05 0.3 1.0 5,0 Frequency (cps) gure 4.48 DYNAMIC YOUNG‘S MODULUS VERSUS FREQUENCY FOR LOW DENSITY ICE AT -IO°C 146 :quency from 0.05 to 0.3 cps. Between 0.3 and 5.0 cps rate of increase is, in general, not as rapid. The rease of dynamic Young's modulus with frequency appears be greater for higher temperatures (—l°C) than for er temperatures (-lO°C). Confining pressure does not ear to have an influence on the relationship between Lmic Young's modulus and frequency. No tests were performed at a frequency of 0.05 on the low density ice samples. The dynamic Young's lus of low density ice increases approximately 4% for ncrease in frequency from 0.3 to 5 cps. For samples temperature of -l and -4°C the rate of increase is :er in the frequency range 0.3 to 1.0 cps than in the a 1.0 to 5.0 cps. For samples at a temperature of 5, the relationship between dynamic Young's modulus requency is almost linear in the range 0.3 to 5.0 Confining pressure does not appear to have an ence on the relationship between dynamic Young's JS and frequency. Effect of Temperature The relationship between dynamic Young's modulus mperature is shown in Figures 4.49 to 4.52 for high y ice and Figures 4.53 to 4.56 for low density ice. lationship is, in general, plotted at four frequen— Dr a given confining pressure. l0._ Figure 4.49 DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR HIGH 147 Frequency Sample density = 0.904 g/cc ZS 0'05 cps Axial strain = 4.4x10-3% ‘5 0.3 cps 13 l.0 cps “.5.0 cps l I l l l J l I I -l —2 -3 -4 -5 -6 -7 —8 -9 Temperature (°C) DENSITY ICE AT A CONFINING PRESSURE 0F 25 PSI I —TO AA 0.3 13 1.0 ‘g_5.0 Frequency "" A 0.05 cps 148 Sample density = 0.904 g/cc Axial strain = 4.4xio‘3z cps cps CPS Temperature (°C) igure 4.50 DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR HIGH DENSITY ICE AT A CONFINING PRESSURE OF 50 PSI Frequency Sample density = 0.904 g/cc 13 0.05 cps " A: 0.3 cps (I 1.0 cps 1‘; 5.0 cps Axial strain = 4.4x10'3z I I I l I I I I fill I -l -2 -3 —4 -5 -6 -7 -8 -9 -10 Temperature (°C) rigure 4.5] DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR HIGH DENSITY ICE AT A CONFINING PRESSURE OF TOO PSI 150 Sample density = 0.904 g/cc " Frequency A 0.05 cps Axial strain = 4.4xio'3z AL 0.3 cps z} l.0 cps ‘; 5.0 cps I I I I I I 41 I I I -T -2 -3 -4 -5 -6 -7 -8 -9 -IO Temperature (°C) gure 4.52 DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR HIGH DENSITY ICE AT A CONFINING PRESSURE OF 200 PSI 151 Frequency Sample density = 0.77 g/cc A 0-3 CPS Axial strain = 4.4xio'3% ll l.0 cps A5.0 cps -l -2 -3 —4 -5 —6 -7 -8 -9 -l0 Temperature (°C) Figure 4.53 DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR LOW DENSITY ICE AT A CONFINING PRESSURE OF 0 PSI 560. 380. 00. 20. . L_ Frequency Sample density = 0.77 g/cc A 0.3 cps Axial strain = 4.4x10‘3z 11 l.0 cps ._ A5.0 cps 1 1 1 1 I I l l l l -l -2 -3 -4 —5 -6 -7 —8 -9 -l0 Temperature (°C) Figure 4.54 DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR LOW DENSITY ICE AT A CONFINING PRESSURE OF 25 PSI A TWO OF V W: Flue: W . Hutu-C) “Mr-CNS): m. IO. Frequency Sample density = 0.77 g/cc L A 0‘3 CPS Axial strain = 4.4xl0'3% A 1.0 cps “b5.0 cps —l -2 -3 -4 -5 -6 -7 -8 -9 —lO Temperature (°C) Figure 4.55 DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR LOW DENSITY ICE AT A CONFINING PRESSURE OF 50 PSI Frequency Sample density = 0.77 g/cc L A0.3 cps Axial strain = 4.4xl0-3% [Ll.0 cps ‘5.0 cps I I I I I I I -1 -2 -3 -4 -5 —6 -7 -8 -9 —lO Temperature (°C) Figure 4.56 DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR LOW DENSITY ICE AT A CONFINING PRESSURE OF I00 PSI 155 The dynamic Young's modulus of the high density anreases with decreasing temperatures. At a confin— >ressure of 25 psi the modulus increases approximately for a temperature decrease from —1 to —4°C. It also Eases approximately 20% for a temperature decrease —4 to -lO°C. The modulus increases more rapidly 1e temperature range -1 to —4°C than in the tempera- range -4 to -lO°C. For the temperature range -4 to I, the rate of increase is almost constant. At low .ning pressures, the rate of increase is slightly :er than at high confining pressures. The frequency :sting appears to have no significant influence on 'elationship between dynamic Young's modulus and rature. The dynamic Young's modulus of low density ice ases approximately 35%for an increase in temperature -1 to —4°C and approximately 20% for an increase in :ature from —4 to —lO°C. The modulus increases : linearly in the temperature range -4 to —lO°C. ite of increase is smaller than for the temperature -1 to —4°C. Frequency and confining pressure appear e no significant influence on the relationship n dynamic Young's modulus and temperature. .5 Effect of Density _______________________ The results presented by Roethlisberger (1972) Bennett (1972) indicate that the dynamic elastic perties of ice vary linearly with density in the range to 0.919 g/cc (refer to Figures 2.11, 2.12, and 2.13, :ion 2.3.2). In the research program the dynamic lg'S modulus was evaluated at two densities: 0.77 and I4 g/cc. The relationship between dynamic Young's .lus and density was assumed to be linear. The rela— ship is shown in Figures 4.57 to 4.59 for three fre— cies at a confining pressure of 50 psi, axial strain .4 X lO_3%, and a given temperature. In Figures to 4.62 the relationship between dynamic Young's Lus and density is shown for three confining pressures frequency of 1.0 cps, axial strain of 4.4 X lO—3%, . given temperature. The dynamic Young's modulus increases approxi- y 60% as density increases from 0.77 to 0.904 g/cc. rature, frequency, and confining pressure do not r to have a significant influence on the relation— 4.5 Damping Ratio of Ice Damping ratio was plotted against the log of strain expressed as a percent as shown in Appendix ures D.l to D.l9, for the high density ice samples _- Frequency Confining pressure = 50 psi AL 0.3 c s . p AXial strain = 4.4xlO_3% 11.1.0 cps “(5.0 cps .0 0.800 0-900 Density (g/cc) gure 4.57 DYNAMIC YOUNG'S MODULUS VERSUS DENSITY OF ICE AT —l°C FOR THREE FREQUENCIES Frequency Confining pressure = 50 psi _ A 0'3 cps Axial strain = 4.4x10‘3 psi 1; l.0 cps ‘5 5.0 cps I I 00 0.800 0.900 Density (g/cc) gure 4.58 DYNAMIC YOUNG'S MODULUS VERSUS DENSITY OF ICE AT -4°C FOR THREE FREQUENCIES 159 Frequency Confining pressure = 50 psi A 0.3 cps Axial strain = 4.4x10'3% 1| l.0 cps 45.5.0 cps l J 3 0.800 0 900 Density (g/cc) Jure 4.59 DYNAMIC YOUNG'S MODULUS VERSUS DENSITY OF ICE AT -IO°C FOR THREE FREQUENCIES APWQ ”Orv WJFJUO—L W.~UC30> UPENC>C l0. I" Confining pressure Frequency = l.0 cps A 0 psi Axial strain = 4.4x10'3z _- A: 25 psi 15 50 psi .. l I ).700 0.800 0-900 Density (g/cc) Figure 4.60 DYNAMIC YOUNG'S MODULUS VERSUS DENSITY OF ICE AT -I°C FOR THREE CONFINING PRESSURES lilliltl‘ IIIIIIIIIIIIIIIIIIIIIIlIIEIlIIlllII!!l!!!!!!!!!!!!!!!!!!!!!!!!!!I!!!!!!!!!!!!!!!llllliifir 1 l6l Confining pressure Frequency = 1.0 cps )II- 15 0 pSi Axial strain - 4.4xl0-3% A; 25 psi )_ A50 psi 13100 psi _\ 700 0.800 0.900 Density (g/cc) DYNAMIC YOUNG'S MODULUS VERSUS DENSITY OF ICE AT -4°C FOR FOUR CONFINING PRESSURES igure 4.6l 162 —- Confining pressure Frequency = 1.0 cps A 0 psi Axial strain = 4.4x10'3z A} 25 psi " A 50 psi 21 l00 psi F__Ai I I 00 0.800 0.900 Density (g/cc) gure 4.62 DYNAMIC YOUNG'S MODULUS VERSUS DENSITY OF ICE AT -IO°C FOR FOUR CONFINING PRESSURES implies . , , H 163 1 Figures D.20 to D.28 for the low density ice. The Ige of damping ratio is from 0.001 to 0.14 for the high lSitY ice and from 0.001 to 0.10 for the low density For a given test condition considerable "scatter" sts in the data. Several reasons for this scatter are an in Section 4.4. In addition to these reasons it is 3 felt that "scatter" occurred in measurements of ping ratio owing to personal error in the measurement :he area of the hysteresis loop. As a consequence of the "scatter" in the data 'e appears to be no identifiable relationship between ing ratio and confining pressure for the majority of samples. Therefore, the data presented reflect only influence of two variables: frequency and tempera- . At a given frequency and temperature the damping as for all confining pressures are presented on the figure. Effect of Strain tude Referring to Figures D.l to D.28, it can be seen there is no pronounced relationship between damping and log percent axial strain. Consequently, it was ad that the relationship between these quantities -near. An assumption of a functional relationship :essary to assess the influence of frequency and 164 nperature on damping ratio. The slope of the "average" raight line of all the data points was established by :aining the least squares best fit line through the data : associated with all test conditions. This is shown Figure 4.63 for the high density ice samples and rure 4.64 for the low density ice samples. The slope the line is 0.1134 for the high density ice and 0.00 the low density ice. The average slopes indicate t the damping ratio of high density ice is affected ghtly by the strain amplitude whereas the damping 10 of low density ice is apparently not affected by strain amplitude. The dashed lines in Figures D.l ).28 represent the least squares best fit line for the . set shown. The solid lines in the figures were n at the average slope through the center of the data for a given test condition. The least squares best line through the center of the data sets for given conditions are summarized in Figures 4.65 to 4.68 :he high density samples and Figures 4.69 to 4.71 for .0w density samples. The relationships are plotted ur test temperatures for a given frequency. The tion of damping ratio ranges from 0.02 to 0.15 for density ice and from 0.016 to 0.08 for low density 165 Sample density 2 0.904 g/cc [3 ZS -3.00 —2.60 —2.20 -I.80 Axial strain (log percent) gure 4.63 LEAST SQUARES BEST FIT LINE FOR DAMPING RATIO OF HIGH DENSITY ICE VERSUS AXIAL STRAIN 166 )— Sample density = 0.77 g/cc A — A A A AA _ A AA A A a A _ A A A A A [£5 [A 2X1 A AAA A A A AAA AA AA A g 13 [A 23 5% 93 A A A A A A % A g 1% Q. A _ u. A M e A % A AA A AA A x A A A @% a AA [Agata A 4% A Ag) - A32: AAAA %A A? A A A AA? see A A i ‘ ' -3.00 —2.60 ‘2°20 Axial Strain (log percent) re 4.64 LEAST SQUARES BEST FIT LINE FOR DAMPING RATIO OF LON DENSITY ICE VERSUS AXIAL STRAIN 167 Temperature A '10C I Sample density - 0.904 g/cc Average results for all con— fining pressures J‘ l l l .00 -2.60 -2.20 -l.60 Axial Strain (log percent) lure 4.65 DAMPING RATIO VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT 0.05 CPS 168 L— Sample density a 0.904 g/cc _ Average results for all con- fining pressures — Temperature LA I 1 1 '3.00 -2.60 -2.20 -I.80 Axial Strain (log percent) gure 4.66 DAMPING RATIO VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT 0.3 CPS Sample density = 0.904 g/cc Average results for all con— fining pressures Temperature —l°C —6°C -lO°C — —4°c A'ZOC 1 1 ' _L -3.00 -2.60 -2.20 -I.80 Axial Strain (log percent) igure 4.67 DAMPING RATIO VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT l.O CPS 170 Sample density 2 0 904 g/cc Average results for all con- __ fining pressures Temperature -lO°C _ -6°C A'4OC - A—ZOC Ame F; 1 1 1 3.00 -2.60 —2.20 -I.8O Axial Strain (log percent) lure 4.68 DAMPING RATIO VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AT 5.0 CPS 171 Sample density = 0.77 g/cc Average results for all con— fining pressure Temperature " -l°C -4°C -lO°C LL 1 . l -3.00 -2.60 -2.20 -l.80 Axial Strain (log percent) igure 4.69 DAMPING RATIO VERSUS AXIAL STRAIN FOR LOW DENSITY ICE AT 0.3 CPS l. 172 Sample density = 0.77 g/cc Average results for all con- )9 _. fining pressure 7 .- Temperature —l°C ) Il- — -4°c -lO°C -3‘00 —.260 '2-20 '1‘80 Axial Strain (log percent) :igure 4.70 DAMPING RATIO VERSUS AXIAL STRAIN FOR LOW DENSITY ICE AT 1.0 CPS 173 Sample density = 0.77 g/cc Average results for all con- fining pressure Temperature -l°C -4°C -lO°C I l l -l.8O -3.00 -2.60 -2.20 Axial Strain (log percent) DAMPING RATIO VERSUS AXIAL STRAIN FOR LOW DENSITY ICE AT 5.0 CPS :igure 4.7l 174 ,5.2 Effect of Frequency The relationship between frequency and damping _tio is Shown in Figure 4.72 for high density ice and gure 4.73 for low density ice at an axial strain ampli- de of 6.35 x 10'3% (loglO = —2.2). The relationship is own at five temperatures (—1, —2, —4, -6, and —lO°C) r high density ice and three temperatures (—1, —4, and 3°C) for low density ice. In general, for the high density ice, damping :io decreases as frequency increases from 0.05 to 1.0 : and increases as frequency increases from 1.0 to 5.0 I. The degree to which the damping ratio follows :se trends, however, appears to be dependent on tempera- e. The greatest decrease in damping ratio in the fre— ncy range 0.05 to 1.0 cps occurs at high test peratures (—l, —2°C); the greatest increase in the quency range 1.0 to 5.0 cps occurs at low test tem— atures (—6, -lO°C). For the low density ice the damping ratio reases as frequency increases from 0.3 to 5.0 cps at 2st temperature of —l°C. Damping ratio decreases as [uency increases from 0.3 to 1.0 cps and increases as [Hency increases from 1.0 to 5.0 cps for test tempera— S of -4 and -lO°C. 175 Temperature L A A -2°c 109 __ ‘ A -4°c A —6°C A —l0°C Sample density = 0.904 g/cc 07 __ Axial strain = 6.35xio'3% Average results for all con- fining pressures __A 1, I l I 0.05 0.3 l.0 5.0 Frequency (cps) lure 4.72 DAMPING RATIO VERSUS FREQUENCY FOR HIGH DENSITY ICE 176 i_ Temperature Sample density 2 0.77 g/cc A—l°C Axial strain = 6.35xio'3% 09 “ 44°C Average results for all con- A—lO°C fining pressure I L7 _- l 6 —- ¥ 1 l l l 0.05 0.3 l.0 5.0 Frequency (cps) lure 4.73 DAMPING RATIO VERSUS FREQUENCY FOR LOW DENSITY ICE 177 .3 Effect of Temperature The relationship between temperature and damping Lo is shown in Figure 4.74 for high density ice and ire 4.75 for low density ice. The relationship is in at four frequencies (0.05, 0.3, 1.0, and 5.0 cps) ghigh density ice and three frequencies (0.3, 1.0, and icps) for low density ice. The damping ratio of high density ice tends to Lng ratio decreases from 0.11 to 0.06 as temperature eases from -1 to —lO°C. The influence of temperature 1all for the frequency range 0.3 to 5.0 cps. The rence between damping ratios for temperatures in ange —l to -4°C is greater than for temperatures a range —4 to -lO°C. At a frequency of 5.0 cps, the 1g ratio appears to increase as the temperature .ses. As shown in Figure 4.75, the influence of tempera- 1 the damping ratio of low density ice is more pro— ! than for the high density ice for the frequency .3 to 5.0 cps. For a frequency of 1.0 cps, the ratio decreases from 0.058 to 0.018 as temperature as from -1 to —lO°C. The effect of temperature I decrease with increasing frequency. The influ— temperature is most significant in the range -1 178 Sample density a 0.904 g/cc L Axial strain = 6.35xio'3% I Average results for all con- ‘5 fining pressure Frequency 13 0.05 cps .. 45 0.3 cps 13 l.O cps 40.5.0 cps ___Al, I I 1 1 Al rill I I I -I -2 —3 —4 -5 -6 -7 -8 -9 -IO Temperature (°C) gure 4.74 DAMPING RATIO VERSUS TEMPERATURE FOR HIGH DENSITY ICE 179 Frequency A03 cps ~09 " ALO cps ALS.0 cps Sample density = 0.77 g/cc Axial strain = 6.34xl0'3% 07 __ Average results for all con- fining pressure L, I I I I I I I I I -I -2 -3 -4 -5 -6 -7 -8 -9 —IO Temperature (°C) :igure 4.75 DAMPING RATIO VERSUS TEMPERATURE FOR LOW DENSITY ICE 180 3 -5°C. At a frequency of 5.0 cps and temperature in 1e range of —5 to —lO°C, the damping ratio appears to Lcrease as temperature decreases. 5.4 Effect of Density A comparison of the damping ratio for the high nsity ice samples and the low density ice samples is own in Figures 4.76 and 4.77. The damping ratio of a high and low density samples is presented as a func- Dn of frequency in Figure 4.76 and as a function of mperature in Figure 4.77. There appears to be no well— fined relationship between density and damping ratio. r damping ratio of low density ice at -l°C is greater In that of high density ice, but at -4 and —lO°C, the Lping ratio of high density ice is, in general, greater n low density ice. At higher temperatures (-1 to —3°C), damping ratio of low density ice is greater than high Sity ice whereas for lower temperatures (-7 to —lO°C) is less than high density ice. .5 Effect of Confining ssure For the majority of the samples tested, there was a well-defined relationship between confining pres— : and damping ratio. However, the test results for a samples were exceptions to this statement. Figure shows the relationship between confining pressure and 181 L. Temperature Axial strain = 6.35xl0'3% Sample density = 0.904 g/cc 0 Average results for all con— "---¢5 '1 C fining pressure -'——A -4°C fl '.IOOC _. Temperature Sample density = 0.77 g/cc <<\ — —O “ICC — -0 “4°C — a ‘10°C I I ' ' .05 ~3 I 5 Frequency (cps) lure 4.76 DAMPING RATIO VERSUS FREQUENCY FOR ICE AT TNO DENSITIES O5 182 Frequency Sample density = O 904 g/cc 45 0.3 cps 1A 1.0 cps A‘s 5.0 cps Frequency Sample density = 0.77 g/cc --- -wed an evaluation of the influence of specific surface 1 (unfrozen water content) to be made. In addition to ie parameters, the effects on dynamic properties ed by variations in temperature, confining pressure, in amplitude, frequency, and number of cycles of ing were considered. 5.2 Test History The test history used in the research program to late the dynamic properties of clay is shown in re 5.1. This test history is, for all practical 185 186 stant temperature A roximate axial strain 3.2 x 10—3% cp=200 psi—- f =0.3 cps —- f=l.0 —o-cp=lOO psi—u- f =0.3 cps —..f=l.0 —>-cp= 50 psi—c»?C =0.3 cps —-.—f =l.O —>-cp= 25 psi—pf =0.3 cps —..f =l.0 -——-cp= 0 psi—..f =0.3 cps —..f =l.O A roximate axial strain 1.0 x 10-2% cp=200 psi._._f =0.3 cps __...f =l.0 —- Cp=lOO psi—miT =0.3 cps ——..f =l.0 —- op: 50 psi-—o-f =0.3 cps —..f =l.0 -—o~ cp= 25 psi—...f =0.3 cps _..f =l.0 '—~ cp= O psi—pf =0.3 cps —..f =l.0 Approximate axial strain 5.6 x 10_2% cp=200 psi _..f =0.3 cps _..f =l.O cp=lOO psi _..f =0.3 cps _,,_f =l.O op: 50 psi _,f =0.3 cps _,.f =l.0 1% roximate axial strain 1.0 x 10- cp=200 psi _..f =0.3 cps _..f =l.O cp=lOO psi__.,_ic =0.3 cps _,_f =l.0 cps cps cps cps cps cps cps cps cps cos cps cps CPS —.—f —.. f "h ‘H , ‘e 5.1 DIAGRAM OF ACCEPTABLE TEST HISTORY FOR FROZEN CLAY =5.0 =5.0 =5.0 =5.0 =5.0 =5.0 =5.0 =5.0 =5.0 =5.0 =5.0 =5.0 CpS CPS cps Ops CpS cps cps cps cps cps CpS cps cps cps 187 ,rposes, equivalent to that for ice. Tests to evaluate .rious test history effects on the dynamic properties of ay were not performed. The ranges of the various test rameters are as follows: (1) (2) (4 v Temperature-~the samples were tested at three temperatures (-l, —4, and —l0°C). The majority of the samples were tested at one temperature only. Seven samples, however, were tested at all three temperatures. Strain amplitude—~the range of strain ampli- 3 l tude was approximately 3.2 X 10— to l X 10- % axial strain. The higher strain amplitudes were dependent on the confining pressure. The maximum strain amplitudes of testing were limited to l X 10_2% for cp = 0 psi and 25 psi, 5.6 x 10'2% for cp = 50 psi, and 1 x 10’1% for cp = 100 psi and 200 psi. The maximum strain amplitudes are associated (approximately) with a tensile failure of the sample or significant sample disturbance. Confining pressure——the samples were tested at five confining pressures (O, 25, 50, 100, and 200 psi). Frequency—-in general, only three frequencies of loading were used in the test program (0.3, 1.0, and 5.0 cps). The O—clay samples 188 at a water content of 36 percent were tested at a very low frequency, 0.05 cps. To inves- tigate the effect of frequencies greater than 5 cps, an O—clay sample at a water content of 29.2%, temperature of —4°C, confining pres- sures of 25, 50, and 100 psi, and strain amplitude of l X 10_2% was tested at 0.3, 1.0, 5.0, 10.0, 20.0, and 50.0 cps. (5) Number of cycles—-for each test condition a sample was subjected to 20 cycles of loading. (6) Water content—-O-clay samples were prepared at four water contents (29.2, 36.0, 46.3, and 55.1%). The M+O-clay was prepared at one T water content (57.2%). 5.3 Influence of Number of Cycles on Evaluation of Dynamic Properties To assess the influence of the choice of the cycle er used to evaluate dynamic properties, the variation the ratio (E at Nth cycle/E at 10th cycle) and (l at CYCle/A at 10th cycle) with number of cycles at dif- ent frequencies, confining pressures, strain amplitudes, temperatures was determined for the O-clay samples. se ratios are shown at l, 5, 10 and 20 cycles in les 5.1 and 5.2. There appears to be no significant iation in the dynamic Young's modulus with number of les for different frequencies, confining pressures, 189 mmm.o o.H NHO.H 0H0.H m.o om Ho.o can mwm.o o.H mHo.H woo.H m.o om Ho.o «1 mmm.o o.H moo.H wHo.H m.o om Ho.o HI wom.o o.H o.H mmo.a m.o om omo.o v: mwm.o o.H mHo.H woo.H m.o om Ho.o an omm.o o.H mmm.o mmm.o m.o om oamoo.o w: o.H o.H o.H NHo.H m.o oom Ho.o vl nwm.o o.H mom.o mHo.H m.o OOH ao.o «I mmm.o o.a mao.a woo.H m.o om Ho.o v1 mmm.o o.H mmm.o voo.a m.o mm Ho.o «1 Hoo.H o.H moo.H moo.H m.o o Ho.o «I ova o.H mmm.o hwm.o o.m om Ho.o v1 mao.a o.H moo.a moo.a o.H om Ho.o «1 mmm.o o.H mHo.H voo.a m.o om Ho.o «I mmm.o o.a o.H hmm.o mo.o om Ho.o «I om 0H m H macho Mo HmQESZ Ammov flammv Amy A0 v hoqmdqwnm whommmum mUDuHHme whouwhmmfimfi macho swoa um.#| @cflcflwcoo aflwuum Hmflxm maowo 52 pm m 190 mmo.H. o.H o.H «HH.H m.o om Ho.o OHI Hmo.H o.H mmm.o mmm.o m.o om Ho.o «I o.H o.H o.H smm.o m.o om Ho.o HI nnm.o o.H o.H NNH.H m.o 00H 0H.o «I o.H o.H o.H o.H m.o OOH wmo.o «I mNo.H o.H o.H NNo.H m.o 00H Ho.o «I mmo.H o.H NNo.H NNo.H m.o OOH meoo.o «I mnm.o o.H mwm.o mNo.H m.o oom Ho.o «I mmo.H o.H o.H mmo.H m.o 00H Ho.o «I Hmo.H o.H mwm.o mma.o m.o om Ho.o «I wHo.H o.H mom.o Nam.o m.o mm Ho.o «I Hmo.H o.H mmm.o mmm.o m.o om Ho.o «I mom.o o.H nmm.o mno.H mo.o om Ho.o «I om mH m H mHo 0 mo HmQESZ AHmmv Amy wowwmwwnm whommwum moduHHme musuwwmwame mHowo QuOH um A mchHmcoo chuuw HMHx¢ wHomo nuz no A l9l ain amplitudes and temperature. At the greatest, the amic Young's modulus at the Nth cycle is approximately % different from the modulus at the 10th cycle. Fur- r, the damping ratio does not appear to vary with the ber of cycles for different frequencies, confining ssures, strain amplitudes, and temperatures. The damp— ratio at the Nth cycle is at most 12% different from damping ratio at the 10th cycle. The dynamic Young's modulus was evaluated from load and displacement channels of the strip—chart order at the 10th cycle by measuring the peak—to—peak litude of the recorded waveform. A typical record for zen clay is shown in Figure 5.2. Hysteresis loops ained from the x-y recorder at the 10th cycle of load- jwere used to evaluate the damping ratio. Typical teresis loops are shown in Figure 5.3. 5.4 Dynamic Young's Modulus of Frozen Clay The dynamic Young's modulus of frozen clay was :ted against the log of axial strain amplitude expressed I percent. The plots are shown in Appendix E. Upon e examination.ofthe test data it was determined that ‘e is no pronounced relationship between Young's modulus "Confining pressure. A typical test reSult which exem— des this is shown in Figure 5.4. The dynamic Young's lus Of an O-clay sample at a water content of 36.0% 192 LUUU \IUI Qure 5.2 TYPICAL RECORD OF LOAD AND DISPLACEMENT OBTAINED DURING CYCLIC TRIAXIAL TESTING OF FROZEN CLAY 193 >30 szomm ..5 wszmz. ._st constant over the range of frequency. Temperature Strain amplitude do not appear to have an influence :he relationship. One frozen O—clay sample at a water content of % was tested at six frequencies (0.3, 1.0, 5.0, 10.0, , and 50.0 cps). The results are shown in Figure . The relationship is plotted from test results at e confining pressures (25, 50, and 100 psi) for a erature of —4°C. It appears from the results shown igure 5.23 that the relationships shown in Figures and 5.22 would be valid up to at least 50 cps. )0. 214 Temperature Water content = 36% " ‘3 ‘1 C Average results for all con- Al -4°C fining pressure III-IO°C I I I I 0.05 0.3 I.O 5.0 Frequency (cps) DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR O—CLAY Figure 5.2l _3 AT AN AXIAL STRAIN 0F 3 l6xl0 % 215 Temperature . __ £3 -I°C Water content = 36% 43 -4°C Average results for all con- fining pressure III-10°C I I I 1 0.05 0.3 1.0 5.0 Frequency (cps) :igure 5.22 DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR O-CLAY AT AN AXIAL STRAIN 0F I.OXIO- % 900. 800. 700. 00. 216 L. Confining pressure Water content = 29.2% A 25 psi Axial strain = 1.0x10'2% A 50 psi Temperature = -4°C (L lOO psi Am A 21 l— I I I I I I 0 3 1,0 5.0 10.0 20.0 50.0 Frequency (cps) Figure 5.23 DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR O-CLAY TESTED T0 50.0 CPS 217 5.4.3 Effect of Temperature The relationship between dynamic Young's modulus and temperature for O—clay at a water content of 36.0% is shown in Figures 5.24 and 5.25. The relationship is plotted at four frequencies (0.05, 0.3, 1.0, and 5.0 cps) at a strain amplitude of 3.16 X 10-3% in Figure 5.24 and 1.0 X 10_l% in Figure 5.25. The dynamic Young's modulus increases signifi- cantly with decreasing temperature. The rate of increase is greater for lower strain amplitude (3.6 X lO—3%) than for higher strain amplitude (1.0 X 10—l%). At a strain amplitude of 3.6 X 10_3%, the dynamic Young's modulus increases sharply from approximately 200 X 103 psi to 700 X 103 psi for a temperature decrease from -1 to —10°C. At a strain amplitude of 1.0 X 10_l%, the dynamic Young's modulus increases gradually from approximately 80 X 103 to 250 X 103 psi for a temperature decrease from -1 to -10°C. The frequency of testing does not appear to influ- ence the relationship between dynamic Young's modulus and temperature. \ 5.4.4 Effect of Water Content The relationship between dynamic Young's modulus ind water content of O-clay samples is shown in Figures 5.26 to 5.31. The relationship is plotted at three fre— [uencies (0.3, 1.0, 5.0 cps) for strain amplitudes of 900. 800. 700. 600. 500. 300. Frequency Water content = 36% —- A 0‘05 cps Average results for all con- A 0.3 cps fining pressure __ ll l.0 cps ‘ 5.0 cps I L I I 1 I I I I I -l -2 -3 -4 -5 -6 —7 -8 —9 Temperature (°C) Figure 5.24 DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR O-CLAY AT AN AXIAL STRAIN 0F 3.16xio'3% 900. 800. 300. 219 Frequency Water content = 36% - ‘3 0'05 cps Average results for all con- ‘5 0.3 cps fining pressure 4; l.0 cps F. IlI 5.0 cps I I I I l I I I I I -l -2 -3 —4 —5 -6 -7 —8 -9 -l0 Temperature (°C) Figure 5.25 DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR O-CLAY AT AN AXIAL STRAIN 0F 1.0x10'1% Dynamic Young's Modulus (103 psi) 900. 800. 700. 600. 500. 400. 300. 200. I00. 220 Frequency Average results for all con- __ A 0.3 cps fining pressure A 1.0 cps A 5.0 cps J I I I I I I I I I 20 30 4O 50 60 Water Conten t (percent) Figure 5.26 DYNAMIC YOUNG'S MODULUS VERSUS WATER CONTENT FOR O—CLAY AT -I°C AND AN AXIAL STRAIN 0F 3.16x10‘3% 900. 500. 221 Frequency Average results for all con- inin _. 15 0.3 cps 9 pressure 21 I.0 cps ‘k Silcps 1 I l I J I I J I I Water Content (percent) Figure 5.27 DYNAMIC YOUNG'S MODULUS VERSUS WATER CONTENT FOR O—CLAY AT -l°C AND AN AXIAL STRAIN 0F 1.0x10'I% lelullllb IUUIIQS I'IOCIUIUS ‘IUv psi) 900. 800. 700. 500. 400. 200. 100. Frequency Average results fOr all con- ‘5 0_3 cps fining pressure “ l.0 cps ‘h 5.0 cps I I I I I I Iii, I 20 30 4O 50 60 Water Content (percent) Figure 5.28 DYNAMIC YOUNG’S MODULUS VERSUS WATER CONTENT FOR O-CLAY AT -4°C AND AN AXIAL STRAIN 0F 3.I6xl0-3% 900. 800. 700. 600. 500. 400. 300. 223 Frequency Average results for all con- _ A 0.3 cps fining pressure (I l.0 cps ,gk 5.0 cps I I I I I, I l I I I IO 20 3O 40 50 60 Water Content (percent) Figure 5.29 DYNAMIC YOUNG'S MODULUS VERSUS WATER CONTENT FOR _O-CLAY AT ~4°C AND AN AXIAL STRAIN OF 3.16 X IO'3% IIVUMIUJ \IU PJI, . y‘all: u 900. 800. 700. 600. 500. 400. 300. 200. I00. -. ll £5 Frequency Average results for all con- — A 0.3 cps fining pressure A l.0 cps A 5.0 Cps . I I I I . 1 I I I l 10 20 30 40 50 60 Water Content (percent) Figure 5.30 DYNAMIC YOUNG'S MODULUS VERSUS WATER CONTENT FOR O-CLAY AT I0°C AND AN AXIAL STRAIN OF 3.I6XIO-3% 900. 800. 700. :600. 500. 400. 225 Frequency Average results for all con- — A 0.3 cps fining pressure 11 l.0 cps IA 5.0 cps .L I I I 1 I I I I I 20 30 4o 50 60 Water Content (percent) DYNAMIC YOUNG'S MODULUS VERSUS WATER CONTENT FOR I Figure 5.3l O-CLAY AT -lO°C AND AN AXIAL STRAIN 0F l.0xlO' % 226 3.15 x 10'2 and 1.0 x 10‘1% and temperatures of —1, -4, and —lO°C. The dynamic Young's modulus increases with increasing water content. The rate of increase is greater for a strain amplitude of 3.16 X 10‘3% than for a strain amplitude of 1.0 X 10—1% at all test tempera- tures. Frequency does not appear to influence the rela— tionship between dynamic Young's modulus and water content. At a water content of 46.3% and a temperature of -10°C, the data points appear to deviate from the trend. The dynamic Young's modulus appears to be smaller than the relationship constructed through the data points for the other three water contents. It is believed that this was associated with melting at the coupling between the sample and the cap and base. Melting of the sample asso— ciated with these data points at the cap and base was observed when the sample was taken out of the triaxial :ell. This was presumably caused by a leak in the rubber membranes surrounding the sample. 3.4.5 Effect of Specific :urface Area Two types of clay with significantly different pecific surface areas were evaluated in the research rogram. The O—clay samples had an estimated specific urface area of 215 m2/g while the M+O—clay samples had 227 an estimated specific surface area of 475 mz/g. The relationship between dynamic Young's modulus and tempera— ture for the two clays is shown in Figures 5.32 and 5.33. The relationship is plotted at two strain amplitudes, 3.2 x 10‘3 and 1.0 x lO_l%, at three frequencies (0.3, 1.0, and 5.0 cps) and a water content of 57.2%. (The results for the O-clay samples at a water content of 57.2% were interpolated from Figures 5.26 to 5.31.) The results shown in Figures 5.32 and 5.33 indi- cate O-clay, with the lower specific surface area, has the higher dynamic modulus. This may be attributed to the higher ice content in the frozen O—clay at a given test temperature. The difference between the modulus for the O-clay and M+O—clay is greater for the high strain amplitude than for the low strain amplitude. 5.5 Damping Ratio of Frozen Clay The damping ratio of frozen clay from the labora- tory test program was plotted against the log of axial strain amplitude expressed as a percent. The plots are shown in Appendix F. An examination of the test results :uggests that no pronounced relationship between damping ratio and confining pressure exists. This is exemplified Iy the relationship between damping ratio and confining Tressure for an O—clay sample at a water content of 36.0% hown in Figure 5.34. The relationship is plotted at four O—clay Frequency Water content = 57-2% A 0.3 CPS Average results for all con- 900. __ 21 1.0 cps fining pressure II. 5.0 cps 800. -— 700. - Eh. “2600. _. In 3 3500. - / é: ; ,a”” a””’ ””’¢) 2400. -‘ ./ / / J I300. ._ é / 200 y / M+0-clay sample . —- 17///’ Frequency 1) 0.3 cps 100. __ (l 1.0 cps I. 5.0 cps 0. _. I I L Jr .1 I I I I I -I —2 —3 -4 -5 —6 —7 -8 —9 -10 Temperature (°C) Figure 5.32 DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR O-CLAY AND M+O‘CLAY AT AN AXIAL STRAIN OF 3.I6xIO-3% 900. 800. 700. 's Modulus (l03 psi) 00 O 0 Dynamic Young N O 0 I00. 4:. O O 229 O-clay Water content = 57.2% Frequency Average results for all con— ._ A 0.3 CPS fining pressure it 1.0 cps III5.0 cps M+O-clay Frequency " (D 0.3 cps () l.0 cps II 5.0 cps I I I I ill I I I I I -l -2 -3 -4 -5 -6 -7 -8 -9 -l0 Temperature (°C) Figure 5.33 DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR O-CLAY AND M+O-CLAY AT AN AXIAL STRAIN 0F I.OXIO—]% Damping Ratio 230 .30 Frequency Water content = 36% '25 13 0.05 cps Temperature = -4°c A: 0.3 cps 21 1.0 cps A; 5.0 cps .20 .l5 .l0 __ .051_ 0, -— J l I I I I 1 I 25 50 75 I00 I25 150 I75 200 Confining Pressure (psi) Figure 5.34 DAMPING RATIO VERSUS CONFINING PRESSURE FOR O-CLAY AT AN AXIAL STRAIN 0F l.0xl0_2% 231 frequencies (0.05, 0.3, 1.0, and 5.0 cps) at a strain amplitude of 1.0 X 10_2% and a temperature of —4°C. It can be seen that damping ratio of frozen clay does not appear to be affected by confining pressure. Therefore, the data presented represent test results associated with all confining pressures at a specific frequency and temperature. In general, the data from two or more sam— ples are available for each test condition. 5.5.1 Effect of Strain Amplitude Referring to Figures F.l to F.48 in Appendix F, the lines in the figures represent the "best fit" lines of the data set for a given test condition. The average "best fit" lines for given test conditions are summarized in Figures 5.35 to 5.49. The relationships between damping ratio and log percent axial strain are shown at a given temperature (-1, -4, and -10°C) and sample water content (29.2, 36.0, 46.3, 55.1, and 57.2%) at three or four test frequencies. The results shown in Figures 5.35 to 5.49 indicate :he damping ratio of frozen clay increases with increasing strain amplitude. The rate of increase of the damping ratio increases with increasing strain amplitude. At a itrain amplitude of 3.16 X 10_3%, the rate of increase is -l (mall; at a strain amplitude of 1.0 X 10 %, the rate of ncrease is great. The damping ratio increases from Damping Ratio .30 .25 .20 .05 L 232 Average results for all confining pressure Frequency _- 0.3 cps " l.0 cps 5.0 cps I I I I I -3.00 ~2.50 -2.00 -l.50 —l.00 -.500 Axial Strain (log percent) Figure 5.35 DAMPING RATIO VERSUS AXIAL STRAIN FOR O-CLAY AT —I°C AND 29.2% WATER CONTENT Damping Ratio 233 ...I .25 - Average results for all confining pressure ‘20 " Frequency 0.3 cps l.0 cps .l5 .. 5.0 cps .lO _. .05 —- .0 - I I I I I —3.00 -2.50 -2.00 -l.50 -l 00 - 500 Axial Strain (log percent) Figure 5.36 DAMPING RATIO VERSUS AXIAL STRAIN FOR O-CLAY AT —4°C AND 29.2% WATER CONTENT ~42 .. .. :31. ..'.‘H’ MTV .30 .25 .20 .05 234 Average results for all confining pressure Frequency _' 0.3 cps l.0 cps 5.0 cps I I I I I -3.00 -2.50 -2 00 -l.50 -l.00 - 500 Axial Strain (log percent) Figure 5.37 DAMPING RATIO VERSUS AXIAL STRAIN FOR O-CLAY AT —I0°C AND 29.2% WATER CONTENT uaulp I ng Rath .30 .25 .20 .05 235 Frequency I. 0.05 cps - Average results for all 0.3 cps confining pressure l.0 cps 5.0 cps _-I I I I I I -3.00 -2.50 -2.00 —l.50 -l 00 -.500 Axial Strain (log percent) Figure 5.38 DAMPING RATIO VERSUS AXIAL STRAIN FOR O-CLAY AT -I°C AND 36.0% WATER CONTENT ”3 nubIU Hun-P I 236 .30 L- '25 " Average results for all Frequency confining pressure 0.05 cps .20 __ 0.3 cps l.0 cps .l5 .. 5.0 cps .lO '- .05 .. I I I I I -3.00 -2.50 -2.00 -l.50 -l.00 -.500 Axial Strain (log percent) Figure 5.39 DAMPING RATIO VERSUS AXIAL STRAIN FOR O—CLAY AT —4°C AND 36.0% WATER CONTENT Damping Ratio .30 .25 .20 .05 Average results for all confining pressure Frequency 0.05 cps 0.3 cps " l.O cps 5.0 cps I I I I I I —3.00 —2.50 —2.00 -l.50 -l 00 -.500 Axial Strain (log percent) Figure 5.40 DAMPING RATIO VERSUS AXIAL STRAIN FOR O-CLAY -IO°C AND 36.0% WATER CONTENT Damping Ratio L. 238 .30 Average results for all confining pressure Frequency .25 - 0.3 cps .20 _. l.0 cps .15 - 5.0 cps .lO _. .05 - .0 - -3.00 —2.50 -2.00 —l.50 -l.00 -.500 Axial Strain (log percent) Figure 5.41 DAMPING RATIO VERSUS AXIAL STRAIN FOR O-CLAY AT -1°C AND 46.3% WATER CONTENT Damping Ratio .30 I- .25 .. Average results for all confining pressure Frequency 0.3 cps .20~— l.0 cps .15.. 5.0 cps .10-— .05.. .0 '- I I I I I —3.00 -2.50 —2.00 -l.50 —l.00 -.500 Axial Strain (log percent) Figure 5.42 DAMPING RATIO VERSUS AXIAL STRAIN FOR O-CLAY AT —4°C AND 46.3% WATER CONTENT Damping Ratio I. 240 .30 .25 .. Average results for all confining pressure .20 _. FrequenCy 0.3 cps l.0 cps 5.0 cps .15 - .lO .. .05 - .0 _. I I I I I -3.00 -2 50 -2.00 -l.50 -l 00 -.500 Axial Strain (log percent) Figure 5.43 DAMPING RATIO VERSUS AXIAL STRAIN FOR O-CLAY AT -10°C AND 46.3% WATER CONTENT Damping Ratio .30 .25 .20 .05 241 Average results for all confining pressure Frequency .. 0.3 cps l.0 cps 5.0 cps I I I I I I -3.00 -2.50 -2.00 l.50 -l.00 -.500 Axial Strain (log percent) Figure 5.44 DAMPING RATIO VERSUS AXIAL STRAIN FOR O-CLAY AT —1°C AND 55.1% WATER CONTENT Damping Ratio .30 - .25 - Average results for all confining pressure .20 __ Frequency 0.3 cps .15 __ l.0 cps 5.0 cps .10 ._ .05 ~— 1 I I I l I -3 00 -2 50 -2.00 -l.50 —l.00 - 500 Axial Strain (log percent) Figure 5.45 DAMPING RATIO VERSUS AXIAL STRAIN FOR O—CLAY AT —4°C AND 55.1% WATER CONTENT uamp I ng Na [1 0 .30 .25 .20 .05 L- 243 - Average results for all confining pressure Frequency 0.3 cps 1.0 cps 5.0 cps I I I I I -3.00 —2.50 -2.00 -l.50 —l.00 -.500 Axial Strain (log percent) Figure 5.46 DAMPING RATIO VERSUS AXIAL STRAIN FOR O-CLAY AT -10°C AND 55.1% WATER CONTENT Damping Ratio .30 .25 .20 .05 L 244 Average results for all confining pressure Frequency .. 0.3 cps l.0 cps 5.0 cps I I I I I I -3.00 —2 50 —2.00 —l.50 -l.00 -.500 Axial Strain (log percent) Figure 5.47 DAMPING RATIO VERSUS AXIAL STRAIN FOR M+O-CLAY AT -1°C AND 57.2% WATER CONTENT Damping Ratio Axial Strain (log percent) .30L Average results for all confining pressure .25 _. Frequency 0.3 cps .20 - 1.0 c s .15 - p .10 _. 5.0 cps .05 - .0 .. I I I I I I —3.00 -2 50 —2.00 -l.50 -l.00 -.500 Figure 5.48 DAMPING RATIO VERSUS AXIAL STRAIN FOR M+O—CLAY AT —4°C AND 57.2% WATER CONTENT Damping Ratio .30 .25 .20 .05 L- 246 Average results for all confining pressure Frequency 0.3 cps 1.0 cps 5.0 cps I I I I I -3.00 -2.50 -2.00 -1.50 —1.00 -.500 Axial Strain (109 percent) Figure 5.49 DAMPING RATIO VERSUS AXIAL STRAIN FOR M+O-CLAY AT -10°C AND 57.2% WATER CONTENT about 3.16 X quency by int 5.49 a of 3.1 -l.0) betwee interp the fa differ 5.512 quency in Fig 247 t 0.02 to 0.3 as strain amplitude increases from "3 to 1.0 x lO_l%. X 10 The relationship between damping ratio and fre- cy, temperature, and water content can be established nterpolating the results presented in Figures 5.35 to at a specified strain amplitude. Strain amplitudes .15 x 10‘3% (loglO = -2.5) and 1.0 x 10_l% (:LoglO = ) were selected for this purpose. The relationships een damping ratio and frequency and temperature were rpolated at a water content of 36.0% only owing to fact that they would be affected only slightly by erences in water content. 2 Effect of Frequency The relationship between damping ratio and fre- :y is shown in Figures 5.50 to 5.52. The relationship -gures 5.50 and 5.51 is plotted at three temperatures -4, and —10°C) and a strain amplitude of 3.16 X l% in Figure 5.51. A , in Figure 5.50 and 1.0 x 10' n clay sample at a water content of 29.2% was tested X frequencies (0.3, 1.0, 5.0, 10.0, 20.0, and 50.0 as shown in Figure 5.52. The relationship is ed at three confining pressures (25, 50, and 100 at a temperature of —4°C. Referring to Figure 5.50 and 5.51, the damping of frozen clay, in general, decreases for an 5 I ..I .20 .30 .25 0T9“! mF-FQEQD IIIIIIIIIIIIIIIII 248 Temperature Water content = 36% ‘5 0 Average results for all con- -1 C fining pressure A —4°C A -lO°C I I I I 0.05 0.3 l.0 5.0 Frequency (cps) ure 5.50 DAMPING RATIO VERSUS FREQUENCY FOR O—CLAY AT AN AXIAL STRAIN 0F 3.16x10'3% 249 lure 5.51 Frequency (cps) DAMPING RATIO VERSUS FREQUENCY FOR O-CLAY AT AN AXIAL STRAIN 0F 1.0x10-]% Temperature Water content = 36% 13 _]0C Average results for all cone fining pressure It -4°C ‘ A -lO°C I I I I 0.05 0.3 l.0 5.0 ‘.r—i 250 Confining pressure Water content = 29.2% . . _ -2,, ‘5 25 psi AXTal strain — lxl0 A Temperature = -4°C 15 50 psi 1; 100 psi AL I I ii I I I 0.3 1.0 5.0 10.0 20.0 50.0 Frequency (cps) re 5.52 DAMPING RATIO VERSUS FREQUENCY FOR O-CLAY TESTED TO 50.0 CPS 251 ease in frequency from 0.05 to 5.0 cps; for frequencies ter than 5.0 cps, damping ratio increases as frequency eases, as shown in Figure 5.52. The rate of decrease imping ratio for an increase in frequency from 0.05 3 cps appears to be slightly greater than for an ease in frequency from 0.3 to 5.0 cps. The damping I gradually increases for an increase in frequency 5.0 to 10.0 cps. In the frequency range 20.0 to cps, the rate of increase is significant. The ence of frequency on damping ratio of frozen clay is er for higher temperatures (—1°C)thanfor lower ratures (—10°C); and is greater for higher strain tudes (1.0 X lO—l%) than for lower (3.16 X lO—3%). Effect of Temperature The relationship between damping ratio of frozen and temperature is shown in Figures 5.53 and 5.54. elationship is plotted at four frequencies for a strain amplitude. The damping ratio of frozen clay decreases Ly for an increase in temperature from —1 to —4°C. an —4 and —10°C the rate of decrease is, in general, : sharp. The decrease of damping ratio is greater )wer frequencies (0.05 cps) than for higher fre- .es (5.0 cps). At a frequency of 5.0 cps, the :nce of temperature on damping ratio appears to be Frequency Water content = 36% £5 0.05 cps Ayerage results for all con- _ A 0_3 cps fInI'ng pressure ll l.0 cps A‘s5.0 cps l l l l l l 1 l l _] _2 -3 -5 -6 -7 -8 -9 '10 Temperature (°C) Figure 5.53 DAMPING RATIO VERSUS TEMPERATURE FOR O-CLAY AT AN AXIAL STRAIN OF 3.16x10’3% AI ‘_ 4—1- Frequency Water content = 36% I: 0'05 cps Average results for all con— AO.3 cps fining pressure _- ll l.0 cps ‘ls5.0 cps l l l l -l -2 -3 -4 -5 -5 -7 -8 _9 _]0 Temperature (°C) I— I— I— — — _ Figure 5.54 DAMPING RATIO VERSUS TEMPERATURE FOR O-CLAY AT AN AXIAL STRAIN 0F l.0xl0']% 254 4 Effect of Water Content The relationship between damping ratio and water ent of the frozen clay samples is shown in Figures to 5.60. The relationship is plotted at three fre- cies (0.3, 1.0, 5.0 cps) for a given temperature and in amplitude. There appears to be no well-defined relationship een damping ratio and water content of frozen clay. s believed, however, that frequency, temperature, and in amplitude may have an influence. The relationship zen damping ratio and water content may be stated as >ws: (1) At a temperature of -l°C and a strain ampli— tude of 3.16 X lO—3%, damping ratio increases slightly for an increase in water content from 29.2 to 55.1% for frequencies of 0.3 and 1.0 cps; but for a frequency of 5.0 cps, damping ratio increases for an increase in water con— tent from 29.2 to 40% and decreases for an increase in water content from 40 to 55.1%. (2) At a temperature of -l°C and a strain ampli- tude of 1.0 X lO_3%, damping ratio increases slightly for an increase in water content from 29.2 to 55.1% for frequencies of 0.3 and 1.0 cps, whereas for a frequency of 5.0 cps damping ratio decreases slightly over the entire range of water contents. Frequency Average results for all confinin res - A 0.3 cps g p sure Al l.0 cps “‘5.0 cps A: [I 20 . 30 4o 50 60 Water Content (percent) igure 5.55 DAMPING RATIO VERSUS WATER CONTENT FOR O-CLAY AT ~l°C AND AN AXIAL STRAIN 0F 3.16Xl0_3% 256 L— Frequency Average results for all 15 0.3 cps confining pressure AL l.0 cps II; 5.0 cps Ah (I l l I l 1 l I I l I 20 30 40 50 60 Water Content (percent) igure 5.56 DAMPING RATIO VERSUS NATER CONTENT FOR O-CLAY AT -l°C AND AN AXIAL STRAIN OF I.OxI.O"% Frequency Average results for all confinin r 55 — A 0.3 cps g p e ure (1 1.0 cps “.5.0 cps ) 20 30 40 50 60 Water Content (percent) ‘gure 5.57 DAMPING RATIO VERSUS NATER CONTENT FOR 0—CLAY AT -4°c AND AN AXIAL STRAIN OF 3.l6xl0—3% L- 258 Fre uenc q y Average results for all ‘5 0.3 cps confining pressure AL l.0 cps 4|.5.O cps A: __ 11 4A 1 l 1 l l I 1 I l 1 Water Content (percent) igure 5.58 DAMPING RATIO VERSUS NATER CONTENT FOR O-CLAY AT -4°C AND AN AXIAL STRAIN OF l.0xl0_]% Frequency Average results for all - 45 0.3 cps confining pressure (I 1.0 cps 45.5.0 cps EEEEEE E As EEEEEE I I I I I I I l I I TO 20 3O 4O 50 60 Water Content (percent) Figure 5.59 DAMPING RATIO VERSUS NATER CONTENT FOR O-CLAY AT -lO°C AND AN AXIAL STRAIN OF 3.l6XlO-3% Frequency Average results for all ‘5 0.3 cps confining pressure It l.0 cps ‘8 5.0 cps l (2:;; D, I l I l I l I l I l 20 3O 4O 50 60 Water Content (percent) gure 5.60 DAMPING RATIO VERSUS WATER CONTENT FOR O-CLAY AT -lO°C AND AN AXIAL STRAIN OF l.OxlO-]% 261 (3) At a temperature of -4°C and a strain ampli- tude of 3.16 X lO_3%, damping ratio increases slightly for an increase in water content from 29.2 to 55.1% for all test frequencies. (4) At a temperature of -4°C and a strain ampli— l tude of 1.0 X 10_ %, damping ratio appears to decrease for an increase in water content from 29.2 to 55.1% for all test frequencies. (5) At a temperature of -lO°C and a strain ampli- 3 tude of 3.16 X 10_ %, damping ratio increases slightly for an increase in water content from 29.2 to 55.1% for frequencies of 0.3 and 1.0; but for a frequency of 5.0 cps, damping ratio decreases slightly with increasing water content. (6) At a temperature of -lO°C and a strain ampli- tude of 1.0 X lO_l%, damping ratio decreases slightly for an increase in water content from 29.2 to 55.2% for frequencies of 1.0 and 5.0 cps; but for a frequency of 0.3 cps, damping ratio decreases for an increase in water con- tent from 29.2 to 40% and increases for an increase in water content from 40 to 55.1%. mperature of ~lO°C, the data points at a water of 46.3% deviate from the others. The sample ted with these results was disturbed, as described ion 5.4.4. 262 5 Effect of Specific ace Area The relationship between damping ratio and tem— ture for O-clay and M+O—clay at a water content of % is shown in Figure 5.61 for a strain amplitude of X 10-3% and Figure 5.62 for a strain amplitude of X lO_l%. The relationship is plotted at three fre- cies (0.3, 1.0, and 5.0 cps). At a strain amplitude of 3.16 X 10_3%, the damp- ratio of M+O-clay is greater than that of O-clay by oximately 0.015. The magnitude of the difference een damping ratio of the two clays does not appear 2 affected by temperature. At a strain amplitude of 1.0 X 10_l% , and fre— :ies of 0.3 and 1.0 cps, damping ratio of M+O—clay :eater than that of O—clay for the temperature range ) —5°C; for the temperature range -5 to —lO°C, the ,ng ratio of M+O—clay is smaller than that of O-clay. frequency of 5.0 cps, the damping ratio of M+O—clay Taller than that of O—clay for all test temperatures. O-clay Water content = 57.2% Frequency Average results for all A 0.3 cps confining pressure A 1.0 cps " ll 5.0 cps M+O-clay Frequency C’ 0.3 cps 01.0 cps” ‘I 5.0 cps -l -2 -3 -4 -5 -6 -7 -8 —9 .10 Temperature (°C) 'igure 5.6l DAMPING RATIO VERSUS TEMPERATURE FOR O-CLAY AND M+O— CLAY AT AN AXIAL STRAIN OF 3.l6xl0'3% 264 L_ O-clay Water content = 57.2% Frequency Average results for all ‘5 0.3 cps confining pressure ll l.0 cps 4‘»5.0 cps M+O-clay - Frequency C) 0.3 cps (I l.0 cps CD 5.0 cps Temperature (°C) 7igure 5.62 DAMPING RATIO VERSUS TEMPERATURE FOR O-CLAY AND M+O- CLAY AT AN AXIAL STRAIN OF l.OxIO—]% CHAPTER VI COMPARISONS OF DYNAMIC PROPERTIES OF ICE AND FROZEN CLAY 6.1 General This chapter presents (l) a comparison of the mic properties of ice and frozen clay obtained in ious studies to those of the present study, and a comparison of the dynamic properties of ice to en clay from the present study. The compression wave velocity and damping ratio appear to be the convenient terms to use as a basis for comparison he results from previous studies to those of the ant study. This is a consequence of the fact that: (l) The P—wave velocity has generally been reported in previous studies. (2 The physical and geometrical characteristics v of the test specimens are known in the pres— ent study that allow a conversion to P—wave velocity to be made whereas they are unknown in several of the previous studies and, hence, would not allow a conversion of the results to dynamic Young's modulus. (3) The damping ratio is easily calculated from the results reported in/previous studies. 265 266 (Converstion equations between damping terms are given in Table 2.1.) P-wave velocity was calculated from the results of present study using: V = / E P D E = dynamic Young's modulus p = material density equation was employed to calculate the P-wave :ity in the cylindrical specimens of the present { because the length of the specimen is much shorter the wavelength of the compression wave which propa- I from the top cap to the bottom cap during cyclic .ng. 6.2 Comparison of Dynamic Properties of Ice . Compression Velocity Figure 6.1 presents the results of the present at two confining pressures and three frequencies function of temperature, together with the results previous studies. It can be seen in this figure the P—wave velocity of the present study is between 3 2.5 km/sec (depending on confining pressure and ancy); the P-wave velocity from previous laboratory After Roethlisberger (l972) (seismic and ultrasonic) ZZ////////////////////Q After Kaplar (l969) (resonant frequency) E \\\ \\\\\\\\\ \\\\\\ :\ Confining requency (cps) pressure . 0 /——f } 200 psi )- / l.0 --—'} 25 psi 3.3 5.0 l.O 0.3 Present Study (cyclic triaxial) 3 Axial strain = 4.4XIO_ % Temperature (°C) igure 6.l P-NAVE VELOCITY VERSUS TEMPERATURE OF ICE 268 [see Figure 2.10, after Kaplar (1969)] is ,mately 3.1 km/sec; the P-wave velocity from : methods and ultrasonic methods [see Figure 2.6, {eothlisberger (1972)] is approximately 3.7 km/ )verall it appears there is a favorable comparison. fference between these three results may be attribu— differences in the test techniques used to measure namic properties. The differences in the test -ques and their influence on the comparison of - velocities are as follows: (1) Strain amplitude-~the strain amplitude of the present study (4.4 X lO—3%) is greater than for the resonant frequency procedure (approximately 1 X 10_4 to 2 X 10-3%) or the geophysical and ultrasonic procedures (approximately 1 X l0_5 to l x 10—3%). It was found in the present study that the elastic modulus of ice decreases with increasing strain amplitude. Therefore, the P—wave velocity of the present study should be lower than the results associated with resonant frequency, geophysical or ultra— sonic procedures. (2) Frequency - the test frequencies in the present study (0.3, 1.0, 5.0 Hz) are much lower than for the resonant frequency 269 procedure (approximately 1 to 1000 kHz), seismic procedure (approximately 150 Hz), or ultrasonic procedure (approximately 50 kHz to 600 kHz). The present study indicates that the dynamic Young's modulus of ice increases with increasing frequency in the range of frequency from 0.05 to 5 Hz. Smith (1969) reports that the modulus increases with frequency in a very high range of fre— quency, 800 to 2800 Hz (see Figure 2.15). Therefore, the low values of P-wave velocity obtained in the present study compared to those obtained by previous researchers seem reasonable owing to the lower frequency of testing in the present study. _ be seen from Figure 6.1 that the influence of 'ature on the P—wave velocity was found to be r in the present study than in previous studies ularly near the melting point. This may be a uence of the fact that the influence of temperature ses with increasing frequency (based on results of esent study) and all of the previous studies are at Lgher frequencies than the present study. Figure 6.2 shows the relationship between P-wave :y at -10°C and density obtained in the present :ompared to the results obtained by Bennett (1972; After Roethlisberger (l972) (seismic and ultrasonic) Temperature = -l6°C Bennett (1972) (ultrasonic) Frequency (cps) 5.0 ____________.——————-——-"-’I.O g . 03 Present Study (cyclic triaxial) Temperature = -l0°C Confining pressure = 59 psi Axial Strain = 4.4xl0' % l l l l I 0.76 0.80 0.84 0.88 0.92 Density (g/cc) Figure 6.2 P-NAVE VELOCITY VERSUS DENSITY OF ICE l 271 Figure 2.12) and Roethlisberger (1972; see Figure ) at —lO°C. The results of the present study are r than those from previous researchers owing to the ons given above and, in addition, to the difference me test temperature of the relationships shown. All 1e results indicate an increase in P-wave velocity density. The rate of increase from the present I is not as steep as the rate of increase obtained revious studies. : Damping Ratio Figure 6.3 shows the relationship between damping and temperature obtained in the present study and elationship obtained by Stevens (1975; see Figure . Ignoring the relationship at 0.05 cps obtained a present study, the comparison appears to be hely favorable. The damping ratios from the present at frequencies of 0.3, 1.0, and 5.0 cps, are in nge 0.023 to 0.045 (with the exception of one point cps and —l°C). The damping ratios obtained by s are approximately 0.033. The average of the damp- tios obtained from resonant frequency tests by (1969; see Figure 2.17) for ice at temperatures 13 to -15°C is approximately 0.0366. The damping f the present study in the frequency range 0.3 to is close to the values obtained from both of the 272 Present Study (cyclic triaxial) Density = 0.904 g/cc _3 Axial strain = 4.4xl0 % Frequency A —-A 0.05 cps --uA 0.3 cps --¢1 1.0 cps -—A 5.0 cps After Smith (l969) (resonant frequency) Average results Temperature = -l3 to —l5°C Density = 0.72 g/cc After Stevens (l975) (resonant frequency) Temperature (°C) Figure 6.3 DAMPING RATIO VERSUS TEMPERATURE OF ICE 273 onant frequency studies. The close comparison may explained by a consideration of the strain amplitudes frequencies of the different test procedures as Lows: (1) Strain amplitude——the strain amplitude of the present study (4.4 X 10—3%) is greater than that associated with resonant frequency procedures. It was found in the present study that the damping ratio of ice decreases with decreasing strain amplitude. Therefore, the damping ratios obtained in the resonant frequency studies should be smaller than those for the present study. (2) Frequency——the frequencies associated with resonant frequency tests are much greater than for the present study. The present study indicates that the damping ratio of ice increases with increasing frequency in the range 1.0 to 5.0 cps. If the increase in damping ratio with increasing frequency is valid up to frequencies of the resonant frequency tests, the damping ratio obtained from the resonant frequency tests should be greater than that of the present study. ore, the combination of the decrease of damping with decreasing strain amplitude and the increase 274 damping ratio with increasing frequency has apparently used the damping ratios from the present study to be ose to those of previous studies, i.e., the effects strain amplitude and frequency tend to cancel each her. 6.3 Comparison of Dynamic Properties of Frozen Clay 3.1 Compression ve Velocity Figure 6.4 shows the relationship between the vave velocity of frozen O—clay and temperature obtained the present study and the results from previous Adies. The P-wave velocity from the present study at axial strain of 3.16 X 10—3% varies from 0.85 to 1.6 ”sec and is equal in magnitude to the results obtained Kaplar (1961; see Figure 2.23) for resonant frequency its performed on frozen Fargo clay. The two relation— ps were obtained at almost the same water content % for O-clay and 35% for Fargo clay). The P—wave ocity for Boston blue clay at a water content of 59% approximately 60% greater than for O-clay at a water tent of 57%. Stevens (1975, see Figure 2.24) con— ted a resonant column test on Goodrich clay at a water tent of 26%. The P—wave velocity is approximately 86% ater than the O-clay of the present study at a water :ent of 57%. Barnes (1963) reported that the P—wave 275 Present Study (O-clay) (cyclic triaxial) ‘ Axial Strain = 3.l6xl0 Frequency ——-A 0.05 cps ___...g( 0.3 cps _3% P- -----43 l.0 cps ""“‘» 5.0 cps After Stevens (l975) " (resonant frequency) Goodrich clay After Barnes (l963) _ o L (seismic) Water content — 26$ / / / I—u / / / ’K After Kaplar (l969) v"’ (resonant frequency) ”" Boston blue clay __ ”” Water content s 59% ’,/' n CO‘YC’e h After Kaplar (l969) (resonant frequency) Fargo clay Water content = 36% Water content = 35% Temperature (°C) Figure 6.4 P-NAVE VELOCITY VERSUS TEMPERATURE OF FROZEN CLAY 276 elocity of alluvial clay obtained by seismic methods is 38 km/sec at a temperature of —2°C. The P-wave :locity is aproximately 70% greater than that of the 'esent study at a water content of 57%. The differences . the test techniques and material types and their ,fluence on the comparison of P—wave velocities is as illows: (l) (2) Strain amplitude—-the strain amplitude for the present study is greater than for the resonant frequency tests. It was found in the present study that the dynamic elastic modulus of frozen clay decreases with increasing strain amplitude for strain ampli— tudes greater than 3.16 X 10—3%. For strain amplitudes less than 3.16 X 10-3% it is felt that there is no change in dynamic elastic properties with strain amplitude. Since the results of the present study presented in Figure 6.4 are for a strain amplitude of 3.16 X 10—3% the difference in the P—wave velocity associated with differences in the strain amplitudes of testing should be negligible. Frequency-—the frequencies associated with resonant frequency tests are much greater than for the present study. The results of V 277 the present study indicate that the dynamic elastic modulus of frozen clay increases with increasingfrequency. Therefore, the P—wave velocity obtained in the present study should be lower than those presented in previous studies. Specific surface area and water content—-in the present study it was found that the P—wave velocity decreased with increasing specific surface area and decreasing water content. Specific surface areas of the clays from the previous studies are not reported, however, liquid limits of the clays are available. The liquid limit is associated with specific surface area; the higher the liquid limit the higher the specific surface area. The liquid limit of the Boston blue clay (47%) is lower than the O—clay of the present study (61%) and the water content (59%) is close to the water content of the O—clay (57%). Therefore, the P-wave velocity of the Boston blue clay should be greater than for the present study. The liquid limit of Fargo clay (68%) is slightly greater than the liquid limit of O-clay and the water con- tent (35%) is nearly identical to the O—clay 278 (36%). Therefore, the P-wave velocity of Fargo clay should be (slightly) smaller than for the present Study. The liquid limit of Goodrich clay (41%) is lower than the liquid limit of O—clay and the water content (26%) is also lower. Based on specific surface area the P—wave velocity should be higher than that for O-clay; based on water content it should be lower. Apparently, the specific surface area has the dominant effect. arall, the values of P-wave velocity obtained in the asent study compared to those obtained in previous 1dies appear to be very reasonable. Damping Ratio Figure 6.5 shows the relationship between damping :io and temperature obtained in the present study and relationship from resonant frequency tests conducted Stevens (1975; see Figure 2.26). The damping ratio ained by Stevens at a frequency of 1 kHz is approxi- ely 0.05. This is of the order of 140% lower than t obtained in the present study at a frequency of 5.0 . The difference in the test techniques and material s and their influence on the comparison of damping 'o is as follows: (1) Strain amplitude—-the strain amplitude for the present study is greater than for the 279 Present Study (cyclic triaxial) Water content = 36% Axial strain = 3.l6xlO' Frequency "—A 0.05 cps ---A. 0.3 cps .....¢g l.0 cps 3% .§ — h~ ‘ ‘- § .~ After Stevens (l975) (resonant frequency) Goodrich clay Water content = 26% Frequency = l kHz 1 1 l l l l l Lilli, J, 11 ~l -2 -3 -4 -5 —6 -7 —8 —9 —l0 Temperature (°C) Figure 6.5 DAMPING RATIO VERSUS TEMPERATURE OF FROZEN CLAY (2 V 280 resonant frequency test. It was found in the present study that the damping ratio of frozen clay increases with increasing strain amplitude for strain amplitudes greater than 3.16 X 10—3%. For strain amplitudes less than 3.16 x 10'3% it is felt that there is no change in damping ratio with strain ampli— tude. Since the results of the present study presented in Figure 6.5 are for a strain amplitude of 3.16 X lO_3% the difference in damping ratio associated with differences in the strain amplitudes of testing should be negligible. Frequency--the frequencies associated with resonant frequency tests are much greater than for the present study. It was found in the present study that the damping ratio decreases with increasing frequency in the range 0.05 to 5.0 cps and increases for fre— quencies greater than 5.0 cps. Stevens (1975) indicates that the damping ratio of frozen silts and sand decreases with increas- ing frequency in the 1.0 kHz to 10 kHz range; he does not comment on the results for frozen clay. 281 (3) Specific surface area—-the influence of spe— cific surface area on damping ratio is not fully understood as explained in Section 5.5.5. arall, it is felt that an explanation of the results )wn in Figure 6.5 is not possible at this time. 6.4 Comparison of Dynamic Young's Modulus of Ice With Frozen Ontonagon Clay :.1 Influence of 'ain Amplitude The relationship between the dynamic Young's ulus of ice and frozen O—clay and strain amplitude is wn in Figure 6.6. The relationship is shown at a perature of —4°C, a frequency of 1.0 cps, four water tents for O-clay (29.2, 36.0, 46.3, and 55.1%), and a confining pressures for the high density ice (0, 25, 100, and 200 psi). The dynamic Young's modulus of Lay increases with increasing water content and the Ilus at a water content of 55.1% approaches the Imic Young's modulus of ice at zero confining pressure. relative relation of dynamic Young's modulus of ice frozen O-clay compares favorably with the relationship ined by Stevens (1973). Stevens indicates that as void ratio of frozen clay increases beyond 1.0 the mic elastic modulus tends to approach that of ice. rate of decreaSe of dynamic Young's modulus of ice _ — — Ice,density a .904 g/cc — O-clay c = \ \Cp=&&i \ <2: . —§§_Q£T wer strain amplitudes. ,4.2 Influence of Frequency The relationship between dynamic Young's modulus ,d log of test frequency for ice and frozen O-clay at strain amplitude of 3.16 X 10-3% is shown in Figure 7. The relationship was plotted at three temperatures 1, -4, and -10°C), a water content of 36% for O-clay, d a confining pressure of 25 psi for ice. The dynamic ung's modulus of ice increases sharply when frequency :reases from 0.05 to 0.3 cps and gradually when fre- ancy increases from 0.3 to 5.0 cps; the dynamic Young's iulus for frozen O—clay increases linearly with the I of frequency in the range 0.05 to 5.0 cps. The rate increase for ice in the range 0.3 to 5.0 cps and izen O-clay in the range 0.05 to 5.0 cps is nearly ntical. .3 Influence of Temperature The relationship between dynamic Young's modulus temperature of ice and frozen O—clay at a strain litude of 3.16 X 10_3% is shown in Figure 6.8. The ationship is shown at four frequencies (0.05, 0.3, , and 5.0 cps), a water content of 36% for O-clay, a confining pressure of 25 psi for ice. The dynamic Ig's modulus of ice and frozen clay increases With 284 O—clav Ice, density 2 0_904 g/cc Water content = 36% Confining pressure = 25 ps1- Temnerature — Temperature —0 -l°C —- A “1°C —0 ‘40C — "A —4°C —. “10°C —-A-IO°C . _‘ /‘/—A——_ _ / ’AP/fl—A a”"¢“————' / _____,_——-A A/ /,4—— ._ /¢ / .\ l l l l 0.05 0.3 1.0 5.0 Frequency (cps) Figure 6.7 DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR HIGH 3 DENSITY ICE AND O-CLAY AT AN AXIAL STRAIN OF 3.12xlO % 285 Ice, density 3 0.904 g/cc Confining pressure = 25 psi Frequency — -A 0.05 cps ___..15 0.3 cps .. ‘-- 13 l.0 cps -- 1“ 5.0 cps _,_.—1| 0-clay Water content = 36% Frequency —0 0.05 cps _____49 0.3 cps .————<) l.0 cps -----4D 5.0 cps Temperature (°C) Figure 6.8 DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR HIGH 3 DENSITY ICE AND O-CLAY AT AN AXIAL STRAIN OF 3.l6xlO- % k 286 :reasing temperature. The rate of increase for frozen slay is greater than that for ice over the entire perature range. At a temperature of —10°C, the dynamic .ng's modulus of frozen O-clay approaches the modulus ice. This is possibly a consequence of the fact that unfrozen water content decreases with increasing perature. 6.5 Comparison of Damping Ratio of Ice With O-Clay .1 Influence of ain Amplitude The relationship between damping ratio and strain litude of ice and frozen O-clay at a temperature of 2 is shown in Figure 6.9. The relationshp was plotted Eour frequencies (0.05, 0.3, 1.0, and 5.0 cps). At strain amplitudes,frequencies of 0.3, 1.0, and 5.0 for ice, and 0.05, 0.3, 1.0 and 5.0 cps for frozen .ay, theldamping ratios are almost equaljximagnitude. ice at a frequency of 0.05 cps, the damping ratio .ow strain amplitudes is approximately 200% greater 1 those associated with other test conditions. The .ificant increase of damping ratio for ice at this frequency (0.05 cps) may be caused by the creep acteristics of ice at low rates of loading. 287 -— — Ice, density £0904 g/cc '— O—clay, water content = 36% Frequency 0.05 cps 0.3 cps l.O cps _ 5.0 cps '— Frequency (cps) 0.05 -——— “” 0 3 ———- 5.0 o’" l.0 "" l l l l l l -3.00 -2.50 -2.00 —l.50 -l.00 -.500 Axial Strain (log percent) Figure 6.9 DAMPING RATIO VERSUS AXIAL STRAIN FOR HIGH DENSITY ICE AND O-CLAY AT -4°C 288 5.2 Influence<1fFrequency The relationship between damping ratio and fre- ancy for ice and frozen O-clay at a strain amplitude 3.12 X 10-3% is shown in Figure 6.10. The relation- .p was plotted at three temperatures (-1, —4, -10°C), 1 a water content of 36% for O—clay. It can be seen lt the influence of frequency in the range 0.3 to 5.0 is similar for ice and frozen O-clay. In the range '5 to 0.3 cps, however, the rate of decrease of damping .io for ice is greater than that for frozen O-clay. .3 InfluenceIDfTemperature The relationship between damping ratio and tem— 3% is shown ature at a strain amplitude of 3.12 X 10— Figure 6.11. The relationship was plotted at four quencies (0.05, 0.3, 1.0, and 5.0 cps), and a water tent of 36% for O—clay. The damping ratio of frozen lay decreases approximately 150% more than for ice r the range of temperature and frequencies of 0.3, y and 5.0 cps. At a frequency of 0.05 cps, the damp— ratio of ice decreases approximately 60% more than damping ratio for frozen clay in the temperature [e -l to —10°C. )7 51 Ice L Density 2 0.904 g/cc \\ Temperature __ ——A -l°C 1‘ \ _. -A -4°C -— A —lO°C \\ \\ 0—clay,water content = 36% \\ Temperature —0 -I°C l l J l 0.05 0.3 1.0 5.0 Frequency (cps) Figure 6.l0 DAMPING RATIO VERSUS FREQUENCY FOR HIGH OENSITV ICE AND O—CLAY AT AN AXIAL STRAIN OF 3.12xio'3% ‘\\\ 290 Ice,density a 0.904 g/cc __ Frequency \ — -A 0.05 cps -—- .15 (3.3 cps _ \ A ‘5 '-- -¢\ l.0 cps -- ~‘st0 cps r- ‘\\\\~ F‘ 0—clay ‘\‘\\~ Water content = 36% Frequency \\\‘\ t. --C> 0.05 cps ““zy --(D 0.3 cps —- '-43 l.0 Ops '--4. 5.0 )— r p. l l l l I I I I l l Temperature (°C) Figure 6.11 DAMPING RATIO VERSUS TEMPERATURE FOR HIGH DENSITY ICE AND O-CLAY AT AN AXIAL STRAIN OF 3.12xlO_3% CHAPTER VII SUMMARY AND CONCLUSIONS Cyclic triaxial tests were performed on labora- ] prepared samples of ice and frozen clay and dynamic Ig's moduli and damping ratios were determined. The : results may be summarized as follows: Dynamic Young's moduli of ice for the densities of ice considered (0.77 and 0.904 g/cc) and range of 3 to 2 X 10—2%), temperature strain amplitude (3 X 10— (—l to —10°C), frequency (0.05 to 5 cps) and confin- (ing pressure (0 to 200 psi) associated with the test program were from 260 x 103 to 900 x 103 psi; damping ratios were from 0.001 to 0.14. The influence of the various parameters on the dynamic Young's modulus of ice are, in the order of their importance: a. Confining pressure—-the dynamic Young's modulus of ice increases with increasing confining pres- sure (1) gradually from 0 to 25 psi (approximately 8%) for high density ice and steeply (approxi— mately 14%) for low density ice, (2) steeply from 25 to 50 psi (approximately 20%) for high density 291 292 ice and slightly for low density ice, (3) gradu- ally from 50 to 100 psi for both ice densities, and (4) only slightly from 100 to 200 psi for high density ice. (Note: no test was conducted at 200 psi for low density ice.) Temperature, frequency and strain amplitude do not appear to have a significant influence on the relationship between dynamic Young's modulus and confining pressure. Density--the dynamic Young's modulus increases approximately 60% as density increases from 0.77 to 0.904 g/cc. Temperature, frequency, strain amplitude and-confining pressure do not appear to have a significant influence on the relation- ship. Frequency——the dynamic Young's modulus of ice increases steeply for an increase in frequency from 0.05 to 0.3 cps. Between 0.3 and 5.0 cps the rate of increase is, in general, not as steep. The increase of dynamic Young's modulus with fre- quency appears to be greater for higher tempera- tures (—1°C) than for low temperatures (-lO°C). Confining pressure, strain amplitude and density do not appear to have an influence on the rela- tionship between dynamic Young's modulus and frequency. 293 Temperature-~the dynamic Young's modulus of high density ice increases with decreasing tempera- ture. At a confining pressure of 25 psi the modulus increases approximately 20% for a tempera— ture decrease from —1 to -4°C. It also increases approximately 20% for a temperature decrease from —4 to —lO°C. The modulus increases more rapidly in the temperature range —1 to —4°C than in the temperature range —4 to ~10°C. The rate of increase at low confining pressures is slightly greater than at high confining pressures. The influence of temperature for low density ice appears to be greater than for high density ice. The dynamic Young's modulus increases approxi- mately 35% for —l to —4°C and in temperature of testing and no significant an increase in temperature from approximately 20% for an increase from —4 to —10°C. The frequency strain amplitude appear to have influence on the relationship between dynamic Young's modulus and temperature. Strain amplitude—-the dynamic Young's modulus of ice decreases only slightly with increasing strain amplitude over the strain range 3 X 10— to 2 x 10‘2%. 3 Strain amplitude apparently has no influence on the dynamic Young's modulus of low density ice. The relationship is apparently 294 not influenced by frequency, temperature, or confining pressure. There appears to be no well-defined relationship between damping ratio of ice and confining pressure or density. The influence of other parameters on the damping ratio of ice is, in the order of their importance: a. Frequency-—in general, damping ratio decreases as frequency increases from 0.05 to 1.0 cps and increases as frequency increases from 1.0 to 5.0 cps. The degree to which the damping ratio fol— lows these trends, however, appears to be dependent on temperature. Temperature—-the damping ratio of ice tends to decrease with decreasing temperature. At a fre— quency of 0.05 cps, the rate of decrease is most pronounced; the damping ratio decreases from 0.11 to 0.06 as temperature decreases from —1 to —10°C. The influence of temperature is small for the frequency range 0.3 to 5.0 cps. The differ— ence between damping ratios for temperatures in the range —1 to -4°C is greater than for tempera- tures in the range -4 to -lO°C. Strain amplitude--the damping ratio of high den- sity ice increases approximately 20% over the 3 2 strain range 3 X 10_ to 2 X 10_ %. Strain amplitude apparently has no influence on the damping ratio of low density ice. The relation- ship is apparently not influenced by other parameters. Dynamic Young's moduli of frozen clay for the two clays considered (specific surface areas of 215 and 475 mZ/g), and range of water content (29.2 to 57.2%), 3 to l X lO-l%), temperature strain amplitude (3 X 10— (-l to -lO°C), frequency (0.05 to 5 cps), and con— fining pressure (0 to 200 psi) associated with the test program were from 90 X 103 to 880 X 103 Psi; damping ratios were from 0.02 to 0.30. The influence of the various parameters on the dynamic Young's modulus of frozen clay are, in the order of their importance: a. Strain amplitude—~the dynamic Young's modulus of frozen clay decreases with increasing strain amplitude. The influence of strain amplitude at the lowest temperature (—10°C) is greater than at the highest temperature (—l°C). At the lowest temperature (-10°C) the modulus decreases steeply (approximately 55%) for an increase in strain 2 to 6 X 10—2%. For strain 3 to 2 x 10—2% amplitude from 2 x 10— amplitudes in the range 3.16 X 10- 2 1 and 6 X 10- to 1.0 X 10_ % the rate of decrease is, in general, small. At the highest temperature 296 (-1°C) there is a gradual decrease in modulus over the entire range of strain amplitudes. The influence of strain amplitude for O-clay appears to be greater than for M+O-clay. The relationship is apparently not influenced by frequency and water content. Temperature-—the dynamic Young's modulus increases significantly with decreasing temperature. The rate of increase is greater for a low strain amplitude (3.16 x 10-3%) than for a high strain amplitude (1.0 X 10_l%). At a strain amplitude 3 of 3.16 X 10— %, the dynamic Young's modulus increases steeply from approximately 200 X 103 3 to 700 X 10 psi for a temperature decrease from —1 to -10°C. At a strain amplitude of 1.0 X 10_l% the dynamic Young‘s modulus increases gradually 3 psi for from approximately 80 X 103 to 250 X 10 a temperature decrease from —1 to -10°C. At a low strain amplitude (3.16 x lo'3%), the influ- ence of temperature for clay at a high specific surface area (475 mz/g) is smaller than for clay at a low specific surface area (215 m2/g); at a high strain amplitude (l X 10_2%), the relation- ship is apparently not influenced by specific surface area. Frequency appears to have no influence on the relationship. The influence of 297 water content on the relationship has not been investigated. Water content——the dynamic Young's modulus increases with increasing water content. The rate of increase is greater at lower strain amplitudes than at higher strain amplitudes. Temperature and frequency do not appear to have a Significant influence on the relationship. Specific surface area-—the lower the specific surface area the higher the dynamic Young's modulus. The difference between the dynamic Young's modulus for O—clay and M+O-clay with different specific surface areas is greater for I high strain amplitudes than for low strain ampli— tudes. At a low strain amplitude (3.16 x lo'3%), the influence of specific surface area at a low temperature (—10°C) is greater than at a high temperature (-l°C); at high strain amplitude (l X 10—2 %), temperature does not appear to have a significant influence on the relationship. The relationship is apparently not influenced by frequency. Frequency——the dynamic Young's modulus of frozen clay, in general, increases slightly for an increase in frequency from 0.05 to 5.0 cps. The rate of increase is almost constant over the 298 range of frequency. (The results from one test indicate the modulus continues to increase only slightly up to 50 cps.) Strain amplitude, tem— perature, water content and specific surface area do not appear to have a significant influence on the relationship. Confining pressure--confining pressure does not appear to affect the dynamic Young's modulus of frozen clay. This conclusion was reached for all test conditions considered. The influence of the various parameters on the damping ratio of frozen clay are, in the order of their impor— tance: a- Strain amplitude--the damping ratio of frozen clay increases with increasing strain amplitude. At a strain amplitude of 3.16 X 10—3%, the rate of increase is small; at a strain amplitude of 1.0 X 10_l%, the rate of increase is great. The damping ratio varies from about 0.02 to 0.3 as strain amplitude increases from 3.16 X 10"3 to 1.0 X lO—l%. The relationship is apparently not influenced by frequency, temperature, water content and specific surface area. Temperature——the damping ratio of frozen clay decreases sharply for an increase in temperature from —1 to -4°C. Between —4 and -10°C the rate 299 of decrease is, in general, not as sharp. The decrease of damping ratio is greater for lower frequencies (0.05 cps) than for higher frequen- cies (5.0 cps). Specific surface area does not appear to have a significant influence on the relationship. The influence of water content on the relationship has not been investigated. Frequency--the damping ratio of frozen clay, in general, decreases for an increase in frequency from 0.05 to 5.0 cps; for frequencies greater than 5.0 cps, damping ratio increases as fre- quency increases. At a low temperature (—lO°C), the influence of frequency on damping ratio is small; at a high temperature (-l°C), the influ- ence of frequency is great. The influence of frequency at a low strain amplitude (3.16 X 10—3%) is smaller than at a high strain amplitude (1.0 X 10_l%). Water content and specific surface area apparently do not have a significant influ- ence on the relationship. Water content-—there appears to be no well-defined relationship between damping ratio and water con— tent of frozen clay. Specific surface area-~at a low strain amplitude (3.16 X lO-3%), the damping ratio is greater for a clay with a high specific surface are than for 300 a clay with a low specific surface area. At a high strain amplitude (1.0 x 10-1%), the influ- ence of specific surface area appears to vary with temperature and frequency. Confining pressure——confining pressure does not appear to affect the damping ratio of frozen clay. This conclusion was reached for all test conditions considered. A comparison of dynamic properties of ice and clay obtained in the present study to those ed in previous studies indicates: 2 P-wave velocity of ice determined in the present Idy is approximately 38% lower than in previous {oratory studies and approximately 64% lower than vious field studies. This may be a consequence Ethe fact that the strain amplitude of testing in 1 present study is greater than those associated previous studies and the test frequencies in the ‘.ent study are much lower than those associated previous studies. (It was found in the present Eeasing strain amplitude and decreasing frequency.) ‘damping ratio of ice determined in the present iy is close to the values obtained in previous iies. The combination of a decrease of damping To with decreasing strain amplitude and an increase 301 3f damping ratio with increasing frequency (as found Ln the present study) has apparently contributed to the close agreement, i.e., the effects of strain amplitude and frequency tend to cancel each other. The P—wave velocity of frozen clay obtained in the present study COmpares very favorably with the results from previous studies. It appears any dif- ferences in P—wave velocities can be explained by differences in the test techniques and material types employed between the present and previous studies. The damping ratio of frozen clay obtained in the present study at a low strain amplitude and 5 cps is approximately 140% higher than that obtained in 1one previous study. Information available at this time is not sufficient to explain this difference. It is felt that the research work reported herein ld be continued using laboratory prepared samples of en silts, sands, and gravels. Information on the ic properties of these soil types, and parameters influence their dynamic properties, could be coupled the results for ice and frozen clay to arrive at a r mechanistic understanding of the dynamic response ozen soils under cyclic triaxial loading. Further, esults from these studies could be used to develop n curves and equations which relate dynamic properties 302 racteristic soil types to index properties and important parameters. Design curves and equations e required to perform ground response analyses zen soil deposits during strong motion earthquakes. LIST OF REFERENCES 303 LIS '1‘ OF REFERENCES ks, E. G. and I. W. Tarshansky. "Soil studies for seismic design of San Francisco transbay tube." Proceedings, Symposium on Earthquake and Vibra- tion Effects on the Behavior of Soils and Foundations. ASTM, San Francisco. 1968. re, B. D. and O. B. Andersland. "The effect of con— fining pressure on the mechanical properties of sand—ice materials." Journal of Glaciology, Vol. 12, No. 66. 1973. re, B. D. ”Mechanical properties of sand-ice materi- als." Ph.D. thesis, Michigan State University. 1972. rsland, O. B. and W. Akili. "Stress effects on creep rates of a frozen clay soil." Geotechnique, Vol. 17, No. 1. March, 1967. rsland, O. B. and I. AlNouri. "Time dependent strength behavior of frozen soils." Journal of the Soil Mechanics and Foundations DiviSlon. ASCE, Vol. 96, No. SM4. July, 1970. rson, D. M. and A. R. Tice. "Predicting unfrozen water contents in frozen soils from surface area measurements." Symposium on Frost Action in Soils, Highway Research Board, Washington, D.C. 1972. as, D. F. "Geophysical methods for delineating perma- frost." Proceedings of the Permafrost Inter- national Conference, National Academy of Sciences, National Research Council Publication No. 1287. 1963. andt, J. C. "Antarctic Peninsula traverse geophysical results relating to glaciological and geological studies." Geophysical Polar Research Center, Research Report Ser. 64—1, Wisconsin University, Department of Geology. 1964. 304 305 :, H. F. "Measurements of ultrasonic wave veloci- ties in ice cores from Greenland and Antarctica." USACRREL Research Report 237. June, 1972. I, C. R. "The structure of Antarctica and its ice cover." In Research in Geophysics, Vol. 2, Solid Earth and Interface Phenomena (H. Odishaw, Ed.), Cambridge, Mass., MIT Press. 1964. R. W. and D. O. Sproule. "Velocity of longitudi- nal vibration in solid rods (ultrasonic method) with special reference to the elasticity of ice." Canadian Journal of Research, Vol. 5. 1931. @, B. and Kohnen. "Ein Beitrag zu den seismischen Untersuchungen auf dem Grénlandischen Inlandeis (Seismic investigations on the Greenland ice sheet)." Polarforschung, Vol. 6, No. 35. 1965. p, B. and H. Querfurth. "Untersuchungen fiber die Elastizitatskonstranten von See und Kunsteis (Investigations of the elastic constants of lake and artificial ice)." Polarforschung, Vol. 5, No. 34, 1/2. 1964. p, B., E. Sorge and K. K. Walcken. "Wissenschaft- liche Ergenbnisse der Deutschen Grénland- Expedition Alfred Wegener 1929 und 1930/31, Band II., Seismik (Scientific results of the German Greenland Expedition Alfred Wegener 1929 and 1930/31, Vol. II, seismic investigations)," Brockhaus, Leipzig. 1933. . J. E. and T. L. Pewe. "Distribution of perma— frost in North America and its relationship to the environment: A review, 1963-1973." North American contribution to the Second International Conference on Permafrost, National Academy of Science. 1973. "Seismic investigations on the northern part of the Greenland ice—sheet." British North Greenland Expedition 1952—54. IV., Geographical Journal, Vol. 122. 1956. G. K. C. "Seismic survey northwest Greenland, 1964." USACRREL Research Report 191. 1966. G. K. C. "Geophysical measurements on the Kaska- wulsh and Hubbard Glaciers, Yukon Territory.“ Arctic Institute of North America Technical Paper 20. 1967. 306 T. N. and C. Echols. "A table of Alaska earth— quakes 1788-1961." Alaska University Geophysics Institute, Research Report 8. 1962. , H. B. and O. B. Andersland. "Predicting unfrozen water contents in frozen soils." Canadian Geo- technical Journal, Vol. 3, No. 2. 1966. , M. B. Introduction to geophysical prospecting, 2nd ed., McGraw Hill, New York. 1960. I, N. C. Research Brief. Soil Dynamics Specialty Session, 7th International Conference on Soil Mechanics and Foundation Engineering, Mexico City. 1969. :h, V. P., J. R. Hall, Jr. and F. E. Richart, Jr. "Large amplitude vibration effects on the shear modulus of sand." University of Michigan Report to Waterways Experiment Station, Corps of Engineers, U.S. Army, Contract DA—22—079—eng—340. October, 1966. :h, V. P., J. R. Hall, Jr. and F. E. Richart, Jr. "Effects of amplitude of vibration on the shear modulus of sand." Proceedings of the International Symposium on Wave Propagation and Dynamic Proper— ties of Earth Materials, Albuquerque, New Mexico. 1967. u, Crary and A. M. Thorn, Jr. "Propagation of elastic waves in ice." Part I, Physics, Vol. 5. 1934. , O. and H. Vidal. "Die Ergebnisse der seismischen Messungen auf dem Hintereisferner in den Oetztaler Alpen 1954 (Results of seismic measurements of Hintereis glacier in the Oetztaler Alps in 1954)," Gerlands Beitr.,Geophys., Vol. 65. 1956. it, R. P. "Study of ice cliff in Nunatarssuag, Greenland." USASIPRE Technical Report 39. 1960. r, R. R. and O. B. Andersland. "Mechanical properties of a sand-ice system." Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 94, No. SM4. July, 1968. B. O. "The nature of damping in sands." Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 91, No. SMl. January, 1965. 307 , B. O. and W. L. Black. "Vibration of normally consolidated clay." Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 94, No. SM2. March, 1968. B. O. and V. P. Drnevich. "Shear modulus and damping in soils: I. Measurement and parameter effects, II. Design equations and curves." Technical Reports UKY 27-70—CE2 and 3, College of Engineering, University of Kentucky. July, 1970. ~ B. O. and V. P. Drnevich. "Shear modulus and damping in soils: design equations and curves." Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 98, No. 8M7. July, 1972. ‘ sley—Smith, G. “Operation Hazen, narrative and preliminary reports 1957-58." Operation Hazen, D, Phys. R (G), Hazen, Vol. 4, Defence Research Board, Ottawa. 1959. :dt, G. "Seismische Versuche aufeiner Eisplatte. (Seismic investigations on an ice plate)," Zeitschrift ffir Geophysik, Vol. 21, No. 1. 1955. I. M. “The Response of earth—banks during earthquakes." Ph.D. thesis, University of Cali— fornia, Berkeley. 1966. I. M. and H. B. Seed. "Seismic response of horizontal soil layers." Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 94, No. SM4. July, 1968. B. "Ice cover and glacial relief." Symposium on Antarctic Research, Wellington, New Zealand (unpublished). 1958. g, H. R. "Geophysical exploration in Alaska." Arctic, Vol. 7, No. 3 and 4. 1954. , H. C. "Application of electro—hydraulic servo control to physical testing." Proceedings of the National Conference on Fluid Power, XVIII, Chicago. October, 1964. . and J. J. Holtzscherer. "Etude des vitesses de propagation des ondes seismiques sur l'Inlandsis du Groenland (Study of the propagation velocity of seismic waves on the Greenland inland ice)," Annales de Geophysique, Vol. 9. 1953. 308 A. and J. J. Holtzscherer. "Determination des epaisseurs de l'Inlandsis du Groenland (Deter- mination of the thickness of the Greenland ice cap)," Annales de Geophysique, Vol. 10. 1954. A. S. "Deep temperature observations in the Canadian North." North American contribution to the Second International Conference on Perma— frost, National Academy of Sciences. 1973. s, A. R. Thermal soil mechanics. Rutgers Uni- versity Press, New Brunswick, New Jersey. 1966. , C. W. "Laboratory determination of dynamic moduli of frozen soils and of ice." USACCREL Research Report 163. January, 1969. , C. W. "Some strength properties of frozen soils and effect of loading rate." Special Report 159, USACCREL. June, 1971. i, H. and A. Takano. "The damping in the dry sand. Proceedings of the 3rd Japan Earthquake Engineer— ing Symposium, Tokyo, Japan, 1970. W. D. "An experimental study of the response of clay embankments to base excitation." Ph.D. thesis, University of California, Berkeley. 1968. R. J. and A. G. Franklin. "Energy dissipation in a soft clay." Proceedings, Symposium on Wave Propagation and Dynamic Properties of Earth Materials, Albuquerque, New Mexico. 1967. M. "Method of determining dynamic properties of visco-elastic solids employing forced vibration." Journal of Applied Physics, Vol. 34, No. 5. 1963. ita, K. H. Kishida and K. Kyo. "Experiments on damping of sands." Transactions of the Archi- tectural Institute of Japan, Summaries of Techni- cal Papers, Annual Meetings of AIJ. 1967. M. "Properties of snow." Cold Regions Science and Engineering (F. J. Sanger, Ed.), USACRREL Monograph III-A1, AD611023. 1964. .- 309 , G. "Geschwindigkeitsbestimmungen elastischer wellen in gefrorenen Gesteinen und die Anwendung akustischer Messungen auf Untersuchungen des Frostmantels an Gefrierschdchten (Velocity determinations for elastic waves in frozen rocks and the application of acoustic surveys for investigation of the frozen zone around a freez— ing shaft)," Geophysical Prospecting, Vol. 9, No. 2. 19961. , Y. and N. H. Fraula. "SOund and shock trans— mission in frozen soils." North American con— tribution to the Second International Conference on Permafrost, National Academy of Sciences. 1973. t, F. E., Jr., J. R. Hall, Jr., and J. Lysmer. "Study of the propagation and dissipation of 'elastic' wave energy in granular soils." Uni— versity of Florida Report to Waterways Experi— ment Station, Corps of Engrs., U.S. Army, Contract DA—22—070-eng-314. September, 1962. G. de Q. "Measurements of ice thickness in Dronning Maud Land, Antarctica." Nature, Vol. 171. 1953. G. de Q. "Seismic shooting and related investi— gations." Glaciology III, Norwegian-British- Swedish Antarctic Expedition 1949—52, Scientific Results, Vol. 5. 1958. .sberger, H. "Studies in glacier physics on the Penney ice cap, Baffin Island, 1953." Part III, Seismic sounding, Journal of Glaciology, Vol. 2, No. 18. 1955. sberger, H. "The applicability of seismic refrac— tion soundings in permafrost near Thule, Green- land." USACRREL Technical Report 81. 1961. sberger, H. "Seismic exploration in cold regions. USACRREL Monograph ll—A2a. October, 1972. v, B. A. "Gliatsiologicheskie issledovania Chetvertoi Antarkticheskoi Ekspenditsii (1959) (Glaciological investigations of the Fourth Antarctic Expedition [1959])," in Materials of glaciological investigations: Chronicle and discussions, Institute Geografii AN SSSR, Issue 4, text in Russian. 1962. N 310 F. S. "The freezing process and mechanics of frozen ground." Cold Regions Science and Engineering Monograph ll—Dl, USACRREL. October, 1969. i. B. Unpublished test results. 1968. I. B. and I. M. Idriss. "Influence of soil condi- tions on ground motions during earthquakes." Journal of the Soil Mechanics and Foundations Division, ASCE, V01. 95, No. SMl. January, 1969. I. B. and I. M. Idriss. "Soil moduli and damping factors for dynamic response analyses." Report No. EERC 70—10, University of California, Berkeley. 1970. [. B. and I. M. Idriss. "Influence of local soil conditions on building damage potential during earthquakes." Journal of the Structural Division, ASCE, Vol. 97, No. 8T2. February, 1971. . and Wilson. "Soil behavior under earthquake loading conditions." State of the Art Report prepared for Union Carbide Corporation, Oak Ridge National Laboratory, Oak Ridge, Tennessee. January, 1972. M. L. and H. B. Seed. "Deformation character— istics of sands under cyclic loading." Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 97, No. SM8. August, 1971. N. "Determining the dynamic properties of snow and ice by forced Vibration." USACRREL Technical Report 216. June, 1969. , H. W. "Viscoelastic properties of frozen soil under vibratory loads." North American contribu- tion to the Second International Conference on Permafrost, National Academy of Sciences. 1973. , H. W. "The response of frozen soils to vibratory loads." USACRREL Technical Report 265. June, 1975. R. J. and D. R. Bacchus. "Dynamic cyclic strain test on a clay." Proceedings, 7th International Conference on Soil Mechanics and Foundation Engineering, Vol. I, Mexico City. 1969. "'3‘ ' 311 or, P. and J. Hughes. "Dynamic properties of foundation sub-soils as determined from labora- tory tests." Proceedings, 3rd World Conference on Earthquake Engineering, New Zealand, Vol. I. 1965. or, R. J. and B. K. Menzies. "Damping characteris— tics of dynamically loaded clay." Proceedings, 4th Australian-New Zealand Conference on Soil Mechanics. 1963. ighi, K. "Permafrost." Journal of the Boston Society of Civil Engineers. January, 1952. L, E., C. R. Bentley, N. A. Ostenso and J. C. Behrendt. "Oversnow traverse programs, Byrd and Ellsworth Stations, Antarctica, 1957-1858." Seismology, gravity and magnetism, IGY Glaci— ological Report Ser. 2, IGY World Data Center A, GlaciolOgy, American Geographical Society. 1959. ., E. and J. Behrendt. "Seismic studies on the Filchner ice shelf, Antarctica, 1957-1958." See Thiel, Bentley, Ostenso, and Behrendt 1959. 1959. , E. and N. A. Ostenso. "Seismic studies on Antarc- tic ice shelves." Geophysics, Vol. 26, No. 6. 1961. en, F. "Die Temperaturabhéngigkeit der P-Wellen geschwindigkeit in Gletschern und Inlandeisen (Temperature dependency of the P-wave velocity in glaciers and continental ice sheets)," Zeitschrift ffir Geophysik, Vol. 33. 1967. s, G. R. "The behavior of saturated clay under seismic loading conditions." Ph.D. thesis, University of California, Berkeley. 1965. 3, G. R. and H. B. Seed. "Cyclic stress—strain characteristics of clay." Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 94, No. SM2. March, 1968. N. C. and G. W. Housner. "Calculation of a surface motion of a layered half-space." Bulletin, Seismological Society of America, Vol. 60, No. 5. October, 1970. 312 rich, N. A. "Mechanical properties of frozen soils." Highway Research Board Special Report § No. 58 (translation from Russian). 1960. M. "Etude de la mer de glace, 4: Le glacier du Tacul (Investigations of Mer de Glace, 4: Glacier du Tacul)," Rapport. Sci. Laboratoire Geophys. et Glaciol. Grenoble, Vol. 102. 1967. T. S. "Cyclic triaxial test equipment to evalu- ate dynamic properties of frozen soils." Report No. MSU-CE-75-l, Division of Engineering Research, Michigan State University, March 1975. D. L. and O. B. Andersland. "Soil—ice Behavior in a model retaining structure." Canadian Geo- technical Journal, Vol. 8, No. l. 1971. J. R. and H. Sandstrom. "Geophysical methods in glaciology." Part II: Seismic measurements on Operation Hazen in 1958, Operation Hazen, D Phys R (G), Hazen, Vol. 6, Defence Research Board Ottawa. 1960. In, G. F. and R. R. Hart. "The damping capacity I of some granular soils." Symposium on 8011 Dynamics, ASTM Special Technical Publication No. 305. June, 1961. S. D. and R. J. Dietrich. "Effect of consolida- tion pressure on elastic and strength properties of clay." Proceedings of the Research Confer— ence on Shear Strength of Cohesive Soils, American Society of Civil Engineers, Boulder, Colorado. 1960. K. "Seismic ice-thickness measurements on Novaya Zemlya, 1932—33." Polarforschung, Vol. 5 (1/2). 1961. APPENDICES 313 APPENDIX A DESCRIPTION OF CYCLIC TRIAXIAL TEST EQUIPMENT 314 APPENDIX A DESCRIPTION OF CYCLIC TRIAXIAL TEST EQUIPMENT Figure A.l shows the cyclic triaxial test equip- developed for the research program. A schematic is n in Figure A.2. The test setup consists of four c components: (1) An MTS electrohydraulic closed loop test system consisting of the actuator, servo- valve, hydraulic power supply, servo con- troller, and hydraulic controller. (This applies a cyclic deviator stress to the sample.) (2) A triaxial cell which contains the sample and non—circulating coolant. (3) A refrigeration unit and cold bath which circulates the coolant around the triaxial cell. (4) Output recording devices to monitor the load (stress)anddisplacement (strain) of the sample during the test. 315 Figure A31. CYCLIC TRIAXIAL TEST EQUIPMENT. Hzmzdgom 5m: ..SxEE. 3.5: “5 oCIx 38550 .30 _o_xu:._.\ fem 05:0.”sz . 5.85“. L a £00 3:828 883530 26E ..8 E L ,.._..p>._ 2322... 535:3: .255 SEEo< 5:22.30 038 22w 222.6; 33013 39.5. nosed 0:306»: toutooom :28 a E w 318 A.1 The MTS Electrohydraulic Closed Loop Test System The heart of the test setup is the MTS electro— hydraulic closed loop testing system. As shown in Figure A.3, it consists of an MTS Model 500.10, 2.8 gpm (0.010 m3/min)/3000 psi (20,700 kN/mz), hydraulic power supply; a Model 436.11 hydraulic control unit with a func- tion generator; a Model 406.11 controller (servovalve con- troller with AC and DC feedback signal conditioning); and a Model 204.61 11 kip (5000 Kg) actuator with a 252.25, 15 gpm (0.057 mZ/min) servovalve and an internal linear variable differential transformer (LVDT). The system operates as follows: (1) A command signal (voltage) from the function generator in the 436.11 or other external source is input to the 406.11 where it is compared to the feedback signal (voltage) from a transducer (e.g., a load cell or LVDT) monitoring the response of the specimen in the closed loop. (2) The difference (error) between the two sig— nals is amplified and applied to the torque motor in the servovalve coupled to the actuator. (3 The torque motor drives a pilot stage which v in turn drives a power stage of the servovalve 319 SOOJO - Hydraulic‘ Servo: Power V°IV° Supply 7 AmpHfied‘ gu:erence Basic SE wien Cbsed Igna s Loop 1436.” HydrouHc 406.H Controller Confro||er Funcfion __%§QED§ES__ Generator Ign umnun Suncno Double Sided Piston ’,.Acluolor LVDT Feedback Signal Frozen Sompm Load CeH Figure A.3 SCHEMATIC OF MTS ELECTROHYDRAULIC CLOSED LOOP TEST SYSTEM 320 which directs hydraulic fluid under pressure to one side or the other of the double-sided actuator piston to cause the actuator to move. (4) The movement of the actuator causes the speci— men to respond in such a way that the trans— ducer monitoring the specimen "feeds back" a signal which is equal to the command signal. The speed at which these steps are executed causes the sample, for all practical purposes, to be subjected to a loading equal to the command signal. A more complete treatment of closed loop testing theory is given by John— son (1964). A.1.1 MTS 406.11 Controller The front panel of the 406.11 controller is shown in Figure A.4. The controls indicated by the circled numbers are discussed in order below. (1) The panel voltmeter has two functions. First, it can be used to indicate the error between the command signal and the feedback transducer. Second, it can be used to indi— cate the voltage output of feedback transducer "XDCRl," XDCR2, or the servovalve drive. (The servovalve regulates the flow of hydraulic pressure between the hydraulic power supply and the actuator.) For the buzzed .EONE Idea 20 30.5035 oz< whompzoo e.< 95m: errnraiari... .. iterator Hurricanufiurnrnflhrfwi... rtfi...wtf...._. .2 .............V . I. . ir».3s.\.l...i. . "In; . I, . \ 0:52 . \ _ / «Sax- . .39.. o :69. o a @iuaoo: .. . so:— 2301 :35 _ ..Uwzo :2: \ I to. _ _ O [.2330 I 321 FUwED t :2: . 322 cyclic triaxial tests a negative error means compression and positive error means tension to the specimen. The panel voltmeter was most often used to monitor the error between the command signal and the feedback trans- ducer before applying the hydraulic pressure. To insure that the actuator does not move when hydraulic pressure was applied, the error signal must be zero. (2) The Set Point control provides a static com— mand signal (voltage). There are 1000 divi- sions on the Set Point dial. Each division is equivalent to 20 mv. A positive command signal (Set Point between 500 and 1000) pro- duces actuator piston compression; a negative command signal (Set Point between 500 and 000) produces actuator piston extension. When the feedback signal is from the LVDT in the actuator, Set Point is used to move the actuator up or down even with no specimen in the loop. When the feedback is from any other transducer the Set Point control estab- lishes a static level of response of the specimen. When feedback was from the LVDT mounted across the sample, Set Point could be used to obtain zero loading on the sample. 323 (3) The Span control establishes the amplitude (4 v of a command signal waveform during cyclic loading. The amplitude is about the Set Point level. There are 1000 divisions on the Span control dial. Each division is equiva— lent to an amplitude of 10 mv. The Span was used to vary the strain amplitude during cyclic triaxial testing. The Gain control establishes the rate and accuracy of response of the actuator ram to the command signal. The Gain control is therefore used to improve the response of the closed loop test system which includes the specimen. To set the system at optimum Gain, the sample was subjected to a low frequency, low amplitude square wave loading. The feed— back signal was monitored with an oscillo- scope. The Gain control was turned clockwise until small oscillations were observed at the peak of the square wave, as shown in Figure A.5b. At this point the Gain was reduced until the oscillations stopped, as shown in Figure A.5c. The Rate (described below) was adjusted to eliminated “overshoot" at the corner of the peak of the square wave as shown in Figure A.5c. a. Over-damped, Gain too low b. Under-damped, Gain too high c. Optimum Gain Figure A.5 GAIN AND STABILITY ADJUSTMENT l (5) (6 v (7) 325 The Rate control helps prevent "overshoot" at high Gain settings. The Rate was adjusted after the Gain had been set as described above. The Feedback Select position determines which feedback signal will be used in the closed loop test circuit. This may be the signal from Transducer Conditioner l (XDCRl), Trans- ducer Conditioner 2 (XDCR2), or from an external transducer conditioner (EXT). The Cal factor, Zero, and Fine/Coarse controls provide adjustment of the signal for trans- ducer used with XDCRl. Cal Factor was used to adjust the voltage output from the LVDT. The Cal Factor was adjusted to obtain i 10 volts when the core of the LVDT moved 0.254 cm. The Zero control introduces an electrical offset to the signal from the LVDT. It has 1000 divisions on the dial. A Zero control setting of 500 corresponds to zero voltage offset. The Zero control provides negative electrical offset when it is between 500 and 000 and positive offset when it is between 500 and 1000. 326 The Fine/Coarse switch determines the operating range for the Zero control. When it is selected to Fine, the electrical off- set from the Zero control per division is lower than when it is selected to Coarse. In this experiment, high electrical offset is necessary therefore the switch was selec- ted to Coarse. (8 The Excitation, Zero, and xl/xlO switch pro— V Vide adjustment of the signal for transducer XDCR2. In general, a load cell was the trans- .ducer used with XDCR2. The Excitation was used to adjust the voltage output from the load cell. It has 1000 divisions on the dial. The Excitation was adjusted to_obtain 25 mv per 10 lbs of loading using a 5 Kip load cell with a sensi- tivity of 2 mv/volt. The Zero control introduces an electrical offset to the signal from the load cell. It has 1000 divisions on the dial. A zero con— trol setting of 500 corresponds to zero voltage offset. It provides positive elec— trical offset when it is between 500 and 000 and negative offset when it is between 500 and 1000. (9 V 327 The xl/xlO switch determines the operating range for the signal from the load cell. When in the x10 position the signal from the load cell is amplified 10 times that of the x1 position. The x1 position was, in general, used in the research program. The Limit Detector determines which trans— ducer conditioner (XDCRl or XDCRZ) signal will be monitored in the "failsafe" circuit. If the switch is set on INTLK the failsafe inter— lock circuit will turn off the hydraulic power supply when the signal voltage is greater or lower than a selected range of voltage. If the switch is set on IND the Limit Detector will indicate by the Upper or Lower red light on the panel when the signal voltage is greater or lower than a selected range of voltage. The Reset is used to extinguish the indi- cator light when the signal voltage level is within the selected range of voltage. If the light for the Limit Detector is still lit with the failsafe interlock circuit in operation, the hydraulic power supply cannot be engaged. Therefore, before applying the hydraulic power supply the light has to be extinguished with (10) (11) 328 the Reset button. If the switch is in the off position the failsafe circuit is inopera— tive. The Upper and Lower limit controls are used to select the range of acceptable voltage. The Upper limit is set at the most positive or least negative limit. The Lower limit is set at the most negative or least positive limit. Each limit dial has 1000 divisions corresponding to 10 volts. Program is used to input an external source of command signal. A.1.2 MTS 436.11 Controller The front panel of the 436.11 is shown in Figure A.6. The controls indicated by the circled numbers are discussed in order below. (1) (2) (3) The Power control applies AC operating voltage to the control unit. The Hyd Pressure Low or High or Hydraulic Off control is used to turn the hydraulic power supply on and off. (The 500.10 hydraulic power supply has no low pressure option.) The PrOgram Stop or Run control is used to start or stop generation of a command signal waveform. 329 ‘: 'W'anwrmi- mmmsngw n -: '5' lg, Iii-31 MTS '- 3' f I 1 GENERATOR I? F—‘PRO' AMfir—HYD PR Efl {— 1’ r—FREOUENCY—l I I ‘ I I I i I I I I I i u Fri-mung MI in. o .quD r \ O . POWER EMERGENCY STOP COUNT INPUT WAVEFORM J F olr i F I a": woo-mm . ‘ . unmn ’\. o .l‘ \l‘ \ (1407‘ o\/‘ I .. \‘ (ND COUN‘ ‘ ~ ~. 0 if I‘LO ‘ii. ‘ .l‘ l. y . . .5“ w . . 13‘ r". «c ,,: {in \. a I a - 3 n a o a e Figure A.6 CONTROLS AND INDICATORS ON 436.ll FRONT PANEL 330 (4) Emergency Stop is used to stop the hydraulic (5) (6) power supply and generation of the command signal waveform. Emergency Stop and Hyd Off have the same effect. The Wave Form control of the Function Genera- tor module is used to select the type of com- mand waveform to be generated. Square, triangular, and harmonic waveforms are available. The Frequency vernier and range selector are used to obtain the desired frequency charac— teristic of the command waveform. Frequencies between 0.01 and 1100 cps are available. A.2 Triaxial Cell A schematic of the triaxial cell inside the cold bath is shown in Figure A.7. The cell is 18 cm in diame— ter and 35 cm high. An aluminum cell was chosen over steel or lucite for three reasons: (1) It has sufficient strength to allow testing (2) (3) at high confining pressure (compared to lucite). It was lightweight for ease of handling (compared to steel). It has a higher thermal conductivity (compared to steel and particularly to lucite) to insure 331 1.55 38 333 .33 £2ng no u:<2mxum m.< 83ml guano 2:32.“. ob :8 33 5.5 “.2235 oEEow :om conoi :oo E25524. ho> 83:52; 8:60 :5... 2:4. {/:00 5300 use 268.. .3333. .21 .38. 238i .5352 on. 332 the noncirculating coolant inside the bath remains at a temperature approximately equal to the coolant circulating outside the bath. Two thermisters were attached to the 7.1 cm diameter, and 17.5 cm high sample to monitor its temperature during the test. An LVDT was attached across the sample to the cap and base to monitor displacement. The output of this LVDT was also the feedback signal in the closed loop dis— cussed in Section A.1. A load cell attached to the base plate of the cell monitors the load. Two copper tubes were connected to the cell at the base plate to apply and monitor pressure in the cell. Pressure to the cell was supplied by a nitrogen pressure tank. As a precaution against pressure fluctuations which might be introduced by movement of the loading rod during cyclic loading, an air reservoir was connected to the pressure line. When applying pressure, coolant which was left in the pressure line could be forced into the cell if air was trapped in the cell. The coolant which would be introduced into the cell would be at a higher temperature than the cell fluid. This could cause variations of temperature during pressure application. To eliminate this problem, a pres— sure line made of copper (high thermal conductivity) was rolled inside the bath to cool the coolant which was trapped in the line. With this system it was found that 333 there was no temperature change during application of pressure. When the LVDT is mounted at the side of the sam— ple, care must be taken to insure that tilt of the sample cap does not influence the displacement reading. A device developed in this research program to eliminate tilt is shown in Figures A.8a and A.8b. It consists of three basic components: (1) A base clamp with a fixed standard for the LVDT body and a connecting rod to the sample cap assembly. (2) An anti—tilt ring connected to the base clamp connecting rod with a piece of spring steel and with a connecting rod for the movable LVDT core. The anti-tilt ring has a diameter 0.63 cm greater than the sample cap to allow free movement about the cap. (3) A top clamp attached to the anti-tilt ring with two spring steel leaves. The spring steel leaves between the anti—tilt ring and the top clamp act as a pivot point. Any (slight) tilt of the sample cap will not be transmitted to the anti—tilt ring through the spring steel. As the sample cap moves, the LVDT core is forced to move because the anti—tilt ring is fixed to the base clamp by the connecting rod. The move- ment at the pivot point causes the displacement measured 334 Ann-t“? Ring Spring Steel Leavesl n Spring Steel I. 0 Top __ Core Clamp aggneciing Connecting ‘_—Rod LVDT Body Connecting —> Rod !--' Base Clamp\ I l a. Schematic of anti—tilt device CoVu await». b. Antiwtilt device Figure A58, ANTI—TILT DEVICE FOR LVDT SIDE MOUNTING. 335 at the LVDT to be twice that of the sample at the center- line. (This is another advantage of the anti-tilt assem- bly since it effectively doubles the output of the LVDT 23‘i for a given sample displacement.) i The vertical displacement of the cap with respect ‘ to the base at the two Spring steel leaves will cause the anti-tilt ring to rotate such that the spring steel at the middle of the ring acts as a pivot point. The move- ment of the anti-tilt ring about the pivot point causes the core of the LVDT to move in both the vertical and horizontal directions. The horizontal component of move- ment causes an error in measuring the strain of the speci- men. To determine the magnitude of the error consider the representation shown in Figure A.9. In the figure, when the two steel leaves move from point C to point D the core will move from point F to point G. Without restraint the core should move vertically for a distance FI. With restraint it moves a vertical distance FH which is shorter than the true vertical movement by an amount HI. To determine the error HI note that for small 6, —AL— AI: (A1) 6A ’ XE ' 2 AB Since 6A = 9E = 6G , 1 GH = EG-e = BF-e = BF-e (A.2) 336 A C a Spring steel leaf pivot point Core position F H Figure A.9 ANTI-TILT DEVICE MOVEMENT DURING CYCLIC LOADING .VGA‘. _ 337 Then HI = GH-eG (A.3) Substituting (A.2) into (A.3) HI = BF'D (A.4) Substituting (A.1) into (A.4) 2 HI = £_LAEL_L§§ (A.5) (AB) 2 in which HI = the error of the anti—tilt device L = the displacement of the sample AB = the diameter of the anti-tilt ring BF = a distance between the edge of the anti— tilt ring and the center of the LVDT core. For the anti—tilt ring used in the research program, AB = 12.22 cm and BF = 3.89 cm. Substituting these values into Equation (A.5) the error associated with the anti— tilt device has been calculated and is shown in Figure A.10. The maximum strain of testing was about 2 X 10-4: cm/cm for ice and l X 10.3 cm/cm for clay. Thus, the maximum error expressed as a percentage of displacement was 0.05 and 0.25%, respectively. [Note: when the dis- placement was approximately 0.07 cm (0.4 percent strain) the core would come into contact with the housing of the 338 8:3 52.23 ME Si 22me was; 22: EmEmsmEz Emfiofiama 7: as; AEU\E0V samuum onEmm moo. woo. moo. moo. Hoo. mooo. HOoo. . q n . «a a a . . _ m O~.< mLzmwm (queoxed) quemeoetdsrp U: 10:13 339 LVDT.] Since this error was relatively small no attempt was made to correct for it in the research program. The two thermisters used to monitor temperature of the sample were calibrated with a laboratory thermome- ter with scale divisions of 0.1°C. The thermisters were capable of reading to the nearest 0.1°C. The temperature of the samples was obtained by averaging the readings of the two thermisters. A.3 Cooling System The cold bath is approximately 0.35 m x 0.35 m X 0.46 m and contains 0.0481n3of circulating coolant, excluding the volume of the triaxial cell. The bath was constructed so that the coolant entered at the bottom and returned to the refrigeration unit from a line at the top of the bath. This is shown in Figure A.ll. It is impor— tant to insulate the top of the cold bath as this repre— sents a potential source of heat loss in the cell (and sample through the cell top plate). Two l-inch thick sheets of styrofoam were used for this purpose. In addi- tion, coolant was "washed" across the top plate of the cell through an auxiliary circulating line. With these precautions it was found that the temperature inside the cell adjacent to the sample did not vary by more than 0.2°C along the length of the sample. To insure that thermal equilibrium had been reached in the specimen and the coolant surrounding it 340 Call with Non-circulatlng Coolant Circulating _ Coolant Cowant Outflow Cold Bath Frozen Coolant lnflow Soil Sample Figure A.ll SCHEMATIC 0F COLD BATH 341 in the cell, temperature measurements were made at the center of several ice and frozen clay samples and adjacent to the sample, as shown in Figure A.12. The figure illustrates the variation of temperature as a function of time for three test conditions. In one test (Figure A.12a), an ice sample and aluminum caps were at an ini- tial temperature of —12.7°C, the coolant inside the cell was at a temperature of —12.2°C. After approximately one hour, the temperature of the sample (measured with a thermister frozen in the center of the sample) and the coolant inside the cell were equal and remained constant. Similar results were obtained when a stainless steel cap and base was used with an ice sample (Figure A.12b) and when an aluminum cap and base was used with a clay sample (Figure A.12c). The temperature of the coolant in the refrigera— tion unit was controlled by a mercury thermometer thermo— stat submerged in the coolant. The temperature difference between the cold bath and refrigeration unit was approximately 0.5°C. Therefore it was possible to set the thermostat in the refrigeration unit and obtain any test temperature desired with reasonable accuracy. A.4 Output Recording Devices The following devices were used to monitor the load cell, LVDT, and thermisters employed in the test program: Temperature Temperature Temperature 342 Sample Temperatur Cell Temperature\ 1| Cell Temperature V Sample Temperature IO '20 3‘0 40 go 60 7b 86 9b Time 0. Variation of temperature of ice using aluminum cap and base -l2 ..3 . Cell Temperature -l4 b Sample Temperature ‘15r ~l6 IO éo $070 50 50 70 ea 90 Time h. Variation of temperature of ice using steel cap and base -lO_ Sample Temperature Cell Temperature To 20% 40 SO 60 70 BI) 90 TTme 0. Variation at temperature of clay using aluminum cap and baee Figure A.12 SAMPLE TEMPERATURE VERSUS TIME FOR DIFFERENT TEST CELLS 343 (1) Transient Recorder (Physical data Model 512 A). (2) x—y Recorder (Varian Associates Model F-80). (3) Strip-Chart Recorder (Sanborn Model 150). (4) 3-1/2 Digit—Digital Multimeter. (5) Oscilloscope. In order to minimize the amount of time required for calibration and monitoring, these devices were connected to a switching panel which, in turn, received the output signals from the load cell, LVDT, and thermisters. The switching panel is shown schematically in Figure A.13. The transient recorder is an electronic instru- ment which accepts and stores analog electrical signals. The signals can be played back repetitively at a selected timebase which may be different from the recording time— base. This allows storage of a high speed event and play— back at a low speed. Two channels are provided to permit storage of two parallel events. The storage is in a digital form in a solid-state, microcircuit memory. The 'duration of recording time can be varied from 100 to 0.01 seconds. The signals are stored in such a manner that all words of storage (2048 words for one event and 1024 words for two parallel events) are stored totally within a recording time of the selected timebase. The transient recorder was used to record load and displacement signals taken during high frequency tests (greater than 0.3 cps) TEMPERATURE Thermistier On P-—— T” on To uurririzfin Bottom From Ext. LVD From lnt. LVDT From Load ‘ Ott TO X-Y RECORDER TO TRANSIENT STORE From ~ Function Otf Generator From Output F'°"‘ OUIPU' From Store Off TO OSCILLUSCOPE From Output X To Osc Y From Store From Function Generator From Store From Output Off Figure A.l3 SCHEMATIC OF CONTROL SWITCHING PANEL 345 and to play them back at slower frequencies on the x-y recorder. It was observed that high frequency, low amplitude sine waves were superimposed on the output signals of load and displacement from the MTS 406.11 controller. This is shown in Figure A.l4a for the output signal displayed on an oscilloscope. The "noise" was approximately 1 to 2 kHz with an amplitude of 80 mv for the displacement signal and 5 mv for the load signal. The noise was produced by the AC Transducer Conditioner in the 406.11 controller which excited the LVDT and the load cell. The x-y recorder and strip—chart recorder could not respond to this high frequency noise, but it was picked up by the transient recorder as shown in Figure A.14a. When this signal was played back to the x—y recorder it caused a "shaking,“ irregular movement of the pen. This movement could also be seen when the signals were displayed on the oscilloscope as shown in Figure A.14b. The effect was more pronounced when the output voltage signals were small compared to the noise. To eliminate this problem, a low pass filter was used on the displacement signal at the input to the transient recorder. The noise on the load signal was low enough to be ignored. The x-y recorder was used to obtain a plot of load versus displacement during cyclic testing. The load cell output was displayed on the y-axis and the LVDT a. 346 dots represent data storage points for transient recorder Typical signal from LVDT at low voltage level. qye from transient store b. Typical hysteresis loop at low strain amplitude of testing. INFLUENCE OF ”NOISE” ON SIGNALS FROM TRANSIENT Figure A.l4 RECORDER 347 output was displayed on the x—axis. The damping char- acteristics of the sample could be determined from this plot as explained in Section 4.3. It was found that the x—y recorder itself created a hysteresis loop when two duplicate sine wave signals from a function generator were monitored on the x—y recorder. This error could be eliminated by adjusting the tension in the wire cable of the slewing system of the recorder. The maximum fre— quency which could be plotted by the x—y recorder without significant hysteresis was approximately 0.3 cps. For higher frequencies of testing, the signals were stored in the transient recorder and played back at frequencies lower than 0.3 cps. Some amplification of the input sig— nals occurred when the transient recorder was used. The amplification appeared to be dependent on frequency. To avoid many calibrations, only damping ratio was deter— mined from x-y recordings. This could be done because damping ratio is a non—dimensional parameter. I The load and deformation at all frequencies of testing were recorded directly on a strip—chart recorder. The frequency response of the strip—chart recorder was checked and it was determined that there was no variation in the amplitude of the input signal when the frequency was varied from 0.05 to 50 cps. The dynamic Young's modulus was determined from the amplitude of load and displacement recorded on the strip-chart. APPENDIX B DESCRIPTION OF SAMPLE COUPLING DEVICE 348 APPENDIX B DESCRIPTION OF SAMPLE COUPLING DEVICE A cohesive unfrozen soil can only be subjected to a very small tensile stress and a cohesionless soil can— not be subjected to any tensile stress. Consequently, no consideration must be made to insure that an unfrozen sample can be subjected to tension during cyclic triaxial testing since this state of stress cannot exist. Cyclic triaxial tests are, therefore, performed on unfrozen soils with the sample always in a compressive state of stress. In contrast to this, ice and frozen soils can be subjec— ted to tensile stresses. Two possible devices to couple the sample to the cap and base to achieve a tensile state of stress were considered in the research program as shown in Figure B.l. The "screw" coupling shown in Figure B.la consists of four screws, 0.64 cm in diameter, in the top and bottom caps. The "screw and metal plate" coupling shown in Figure B.lb is essentially the same as the “screw" cou— pling except an aluminum plate, 5.4 cm long, 2.54 cm wide and 0.64 cm thick was attached to two of the screws in the top and bottom caps. The clearance between the cap and the aluminum plate was set at 1.27 cm. 349 Four screws sample Figure 8.1 350 b. Four screws and metal plate Total length sample I Effective length COUPLING DEVICE USED IN CYCLIC TRIAXIAL TESTING OF ICE AND FROZEN CLAY 351 Figure B.2 shows a comparison of the hysteresis loops obtained for an ice sample without a coupling and for ice samples with the "screw" and "screw and metal plate" couplings. The hysteresis loop for the sample without a coupling is highly non-symmetric. This is reasonable since the sample can only be subjected to compressive stresses. The minimum deviator stress is equal to 12.8 psi; it is not equal to the confining pressure, 25 psi. There are two possible explanations for this discrepancy: (l) The sample did not separate from the caps ,1 l t i 1 because the sample elongated owing to the confining pressure acting on the side of the sample. As a result of the sample elongation there was an axial stress in the sample which would be measured as the devi— ator stress, 12.8 psi. (2 v The sample separated from the cap but the membrane did not penetrate into the gap. Consequently, there was an air pressure in the gap less than the confining pressure. (If the membrane penetrated through the gap between the sample and the cap the minimum deviator stress would be zero.) The minimum deviator stress, 12.8 psi, would be equal to 352 mmugmm wzzmzou ...zmmmmbo mo..— mfisfim H: mo moon: mHmmmmHmE 453:. N.m whom; an... .22: 23 .323 .58 £3 33:8 28E: 3. A3 not SOLaw _v_x< NQEMS neonw I 30 n. u 333...... can: n 2396960» .N._n .2. nu u 2:303 mEczcoo dew 3%: . 825 3.230 also” ~50. «£3 v0.5.0... oEEon 02 Any :wmn- whm r SS . 588 E: .843 nexmnm .95.? I n3 n. n xocozuveu Ono" .. n EEEXEok .maouuesnmwa 055.80 0.3 :2: 322m .2230 9:338 32:? case» 3. 2: 38 R 525 3:3 w.~T TOURS. MQmem 1 .8 n; moan—scorn. coo... u 852352. Egon u 832:. "Eczcoo :2: 39.5 33:60 353 a reduction of the confining pressure, 25 psi, by a pressure of 12.2 psi in the gap. The hysteresis loop for the sample with the "screw" coupling is also highly non-symmetric. This indicates (l) the sample failed, (2) the dynamic modulus in compression is much greater than that in tension, or (3) the coupling was not sufficient to resist the tensile force applied. Inspection of the samples from the tests with this coupling indicated they had not failed. There is no reason to believe the modulus in tension for ice is significantly different than the modulus in compres— sion. Thus, the hysteresis loop could not be explained on this basis. Therefore, it was concluded the coupling did not provide sufficient resistance to the tensile force. The screw coupling was rejected for this reason. The hysteresis loop for the sample with the four screws and metal plate is symmetric and indicates that a resistance to the tensile force was developed which allowed the sample to be subjected to a tensile stress. This coupling was selected for use in the research program. It is obvious that with the "screwzuuimetal plate" coupling the effective length of the sample used to cal- culate dynamic properties would be slightly less than the total length of the sample. The effective length of the sample is extremely difficult to calculate because it is 354 dependent on the dynamic elastic moduli of the specimens. Therefore, for practical purposes, the effective lengths were assumed to be 2.54 cm shorter than the full length, owing to a reduction of 1.27 cm from the top cap and 1.27 cm from the bottom cap. Even if the effective length is slightly in error it would reSult in only a small error in the evaluation of the dynamic modulus and axial strain. The lengths of the specimens were approximately 18 cm with corresponding effective lengths of about 15.5 cm. If the assumed effective length was i 1 cm in error, the error in the dynamic modulus would be about 6.5% and the error in the strain would be about 7%. 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