ESTIMATION OF THE ORIGINAL SHEAR STRENGTH OF DEEP SEA SEDIMENTS FROM ENGINEERING INDEX PROPERTIES by Robert Wyman Hoag II ! United States Naval Postgraduate School THESIS ESTIMATION OF THE ORIGINAL SHEAR STRENGTH OF DEEP SEA SEDIMENTS FROM ENGINEERING INDEX PROPERTIES by Robert Wyman Hoag II September 1970 Tkl& document ha& been appiovcd Ion. public kz.- IzcL&e. and 6alt; i£i> dJUviibuXJuon ti> imturuXe.d. TJ.35603 1l postgraduate school TEEEY, CALIF. 93940 Estimation of the Original Shear Strength of Deep Sea Sediments from Engineering Index Properties by Robert Wyman^Hoag II Lieutenant Commander, United States Navy B. S., United States Naval Academy, 1961 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN OCEANOGRAPHY from the NAVAL POSTGRADUATE SCHOOL September 1970 vi^uu^ tfsrtt e./ ABSTRACT Multiple linear regression techniques were employed in a statistical analysis of data from 114 deep sea cores in order to derive an equation for predicting shear strength from sediment engineering index properties. Water content, depth of burial, liquid limit, and plastic limit proved to be the only factors significantly influencing the strength in these cores. The multiple and individual correlation coefficients between these four parameters and the logarithm of shear strength proved to be higher than the coefficients computed in a linear strength relation. Additionally, other regression analysis were conducted to determine a water content pre- diction equation and to investigate correlations among other sediment properties. Water content is shown to be highly correlated with liquid limit. Ancillary to the above analysis, tests were conducted to determine the degree of reproducibility of original liquid limit values from dried sediment material. I . INTRODUCTION TABLE OF CONTENTS 9 A. OBJECTIVE - 9 B. DISCUSSION "" 9 q 1. General -------------- 2. Parameters ----------------- a. Depth in the Core 12 b. Median Grain Size 13 c. Water Content -- ----- -- 13 d. Liquid Limit " " 14 e. Plastic Limit - 16 f. Plasticity Index 16 g. Liquidity Index 17 3. Other Investigations 18 II. REPRODUCIBILITY OF PARAMETERS - - - 20 A. DISCUSSION * " 20 B. LIQUID LIMIT 20 1. Background -------------- *w 2. Test Procedures ------------- *■* 3. Test Results ---------------- 22 C. OTHER PARAMETERS 25 1. Depth in the Core 25 2. Water Content ------- - - -26 3. Median Grain Size 26 4. Plastic Limit 26 III. DATA 27 A. INITIAL REQUIREMENTS AND LIMITATIONS 27 B. GENERAL 28 IV. STATISTICAL ANALYSIS 43 A. METHOD - 43 1. Regression Analysis ------------ 43 2. Confidence Limits - - --------- 43 B. STATISTICAL RESULTS 44 1. Shear Strength and Water Content Equations - 44 2. Other Correlations ------------- 52 a. Liquidity Index - Logarithm Sensitivity 52 b. Liquid Limit - Water Content ----- 54 V. CCNCLUSIONS AND RECOMMENDATIONS 58 A. CONCLUSIONS 58 B. RECOMMENDATIONS 58 APPENDIX A DATA ANALYZED 60 BIBLIOGRAPHY - - 98 INITIAL DISTRIBUTION LIST - 102 FORM DD 1473 103 LIST OF TABLES I Table I. Liquid Limit Test Results ---------------23 II. Positions of Naval Civil Engineering Laboratory Cores - 30 III. Positions of Cores from a Technical Report ------ -32 IV. Positions of National Oceanographic Data Center Cores - 33 V. General Sediment Parameter Statistical Information - - 39 VI. Shear Strength Correlation Coefficients --------45 VII. Correlation Coefficients for Depth in the Core - - - - 46 VIII. Water Content and Liquid Limit Correlation Coefficients with Other Parameters ---------- 57 (o LIST OF ILLUSTRATIONS Figure 1. Shear Strength versus Depth for Various Depositional Areas ----------- ------~ 12 2. Liquid Limit Device --- 15 3. Consistency Limits ------------------ 16 4. Plasticity Chart for Sediment Samples Used in the Liquid Limit Tests --------------- - "24 5. Atlantic Ocean Core Locations -------------34 6. Gulf of Mexico Core Locations --- --- -35 7. Pacific Ocean Core Locations 10. Shear Strength Histogram 36 8. East Pacific Core Locations -- ' ' 37 9. Kamchatka Peninsula Core Locations - -38 40 11. Water Content Histogram --------------40 12. Liquid Limit Histogram -------- ------ 41 13. Plastic Limit Histogram ----------- "41 14. Median Grain Size Histogram "42 15. Sensitivity Histogram 42 16. True versus Computed Shear Strength ----- -47 17. True and Computed Shear Strengths versus Depth in the Core ------------------""""" 18. True versus Computed Water Content ----------- 19. Liquidity Index versus Sensitivity Relationship 53 20 Water Content versus Liquid Limit Relationship - - - 5 ACKNOWLEDGEMENTS Appreciation is expressed for the suggestions of Professor R. J. Smith under whose direction this investigation was conducted. Miss Georgia Lyke of the Naval Postgraduate School Library provided able assistance in locating reference materials, and Mr. G. P. Learmonth of the W. R. Church Computer Facility advised concerning computer techniques on numerous occasions. Personnel of the Site Development and Foundation Engineering Divisions of the Naval Civil Engineering Laboratory, and particularly Mr. M. C. Hironaka and Mr. D. G. Anderson provided useful data and helpful comments. The Naval Facilities Engineering Command interest in, and support of the marine sediments research at the Naval Postgraduate School deserves special recognition. 8 I. INTRODUCTION A. OBJECTIVE The primary objectives of this investigation were twofold. First, to develop an equation for the prediction of the original shear strength of deep sea sediments from water depths greater than 6000 feet utilizing their engineering index properties as determined from partially dry sediment cores. From such an equation it is possible to make an estimate of the approximate load-bearing capability of the sediment in a particular oceanic area without conducting a sampling and testing program (Hironaka and Smith, 1969). The second objective was to examine the several possible methods of evaluating the liquid limit of marine sediments to determine the reproducibility of the original value. B. DISCUSSION 1. General For many years various institutions and agencies have been collecting deep sea sediment samples for a variety of scientific investigations. Very few of these cores, however, have been analyzed from an engineering stand- point to determine their mass physical properties. Though such samples have proven useful for their intended purpose, a considerable amount of engineering type data has essentially been lost. Many of these cores have been stored for subsequent examination and are available for the determination of those index properties which are presumably not affected by the material being in a dry or remolded condition. It has therefore been hoped that various re- lations could be developed between the reproducible index properties and the original engineering properties of the sediment. Index properties are generally defined as those parameters which classify the sediments qualitatively into groups having similar soil engine- ering properties. Engineering properties, on the other hand, can only be determined on undisturbed samples, and define specific characteristics of the soil which are directly related to its bearing capacity. Shear strength is currently the most important engineering property of marine sediments from the standpoint of foundation design and bearing capacity calculations. Tschebotariof f (1951) derives the following equation for com- puting bearing capacity from shear strength: BC - 5.52c (1 + 0.38h/b + 0.44b/L) (1) BC = Bearing capacity (load per unit area) c ■ Cohesion per unit area h = Depth of burial of foundation b ■ Width of foundation L = Length of foundation For saturated cohesive soils such as marine sediments, it is generally assumed that the angle of internal friction is zero, therefore shear strength equals cohesion (Richards ,1961) . The above equation has been used in at least one deep-sea foundation study (Hironaka and Smith, 1969). At present the easiest and most practical method of measuring shear strength is by use of the vane shear device. This is a standard piece of soil mechanics laboratory equipment, and modifications for its use at sea have been developed at the Naval Postgraduate School (Heck, 1970). In working with dried sediment samples, however, it is impossible to directly measure the original shear strength of the material as it existed in its naturally saturated state. It is therefore necessary to establish some 10 type of relationship, perhaps statistical, between shear strength and certain reproducible sediment properties. Such a value could then be used at least as a preliminary estimate of shear strength for use in equation (1). Application of an equation relating shear strength with index properties would be particularly valuable in the computation of sediment bearing capa- city for several types of situations, provided a stored core is available from the general area of interest. An example is, loss of an object (such as a submersible) in mid-ocean under conditions where it is immediately necessary for search purposes to know the bearing capacity of the sediment. Application of a shear strength prediction equation, along with data obtained from an available desiccated core could provide a rough estimate in a matter of hours, whereas it might be several weeks before a research vessel could arrive on the scene to core and then test the sediment. A considerable amount of money could also be saved by alleviating the necessity for a detailed coring and foundation study program in the emplace- ment of some unmanned experiments on the deep sea floor. The one basic assumption made before the onset of this investigation was that all index properties are reproducible, even after the sediment has once been dried. Considerable doubt does exist, however, regarding this as- sumption. In conjunction with the statistical analyses, experiments were conducted to determine the degree to which one of these index properties was reproducible. 2. Parameters Prior to commencing a statistical study of the available existing data, a survey of the technical literature was made to determine which of 11 the sediment properties have been found by other researchers to influence shear strength. In order to check for possible correlations and interrela- tionships among the various parameters, several index properties not identi- fied in this survey were also included in the overall analysis. The properties investigated are described below, a. Depth in the Core Some investigations have indicated a general correlation be- tween shear strength and depth below the sea floor-water interface for normally consolidated sediments (Arrhenius, 1952; Richards, 1961; Bjerrum, 1954) . Figure 1 from Moore (1961) shows the strength versus depth relation- ships for sediments from various depositional environments. The overall trend, though variable due to non-homogeneity of the sediment column, re- sults from increasing overburden pressure as sedimentation continues. McClelland (1956) presents an excellent basic discussion of this general subject. 1. N. Pacific (MOORE, 1961) 2. E. Pacific (Arrhenius, 1952) 3. Gulf of Mexico "j 4. Gulf of Mexico I Fisk and 5. Miss. River Delta) McClelland (1959) 10 20 30 40 50 60 BURIAL DEPTH ( meters ) 70 80 Figure 1. Shear Strength versus Depth for Various Depositional Areas (Moore, 1961) 12 b. Median Grain Size The effect of grain size distribution on the shear strength of fine grain sediments is not well defined, however, it does give some measure of the consistency of the material. Trask and Rolston (1951) con- ducted a comprehensive study of this effect and concluded that for a given water content, the strength increased with an increasing percentage of fine grained clay-sized particles. Analyses of 24 cores from the Hatteras Abyssal Plain by Stiles (1967) demonstrated that mass properties were affected to a greater degree by grain size than any other parameter. One study of fine grain bay sediments showed that shear strength had a positive correlation with grain size (Keller, 1964). However, since an inverse relationship exists between grain size and water content (Trask and Rolston, 1950) it is probable that the decrease in water content as a result of the larger grain size was the dominant factor in the higher shear strengths which were noted. Though not considered in this study, the mineralogic type of clay for a given grain size is also an important factor (Trask and Rolston, 1951). As the grain size increases, however, the specific type of mineral becomes a less influential factor relative to shear strength (Winslow and Gates, 1963). c. Water Content Water content has long been recognized as one of the major factors which affect the shear strength of sediments (Richards, 1962). Trask and Rolston (1950) show that an inverse relationship exists (for specific grain size groups) between water content and the logarithm of shear strength of the San Francisco Bay sediments. A similar result was found by Morelock (1969) for Gulf of Mexico sediments, however, Holmes and Goodell (1964) indicate that a linear relation exists. Richards and Keller 13 (1962) suggest that it may eventually prove possible to determine shear strength from in-situ values of water content. The water content usually decreases with increased depth in the sediment (Richards, 1962), which equates well with a decrease in the void ratio with increased overburden pressure so as to permit the sediment to hold a lesser quantity of water. In that the void ratio is in turn dependent on grain size (Rominger and Rutledge, 1952) this results in a general dependency of water content on both grain size and depth in the core. A combination of these results verifies an inverse relation between shear strength and water content, d. Liquid Limit The liquid limit is the water content, expressed in percent- age of dry weight, at which a remolded soil is just capable of resisting a shearing force caused by several sharp impacts. It is generally considered to represent the boundary between the viscou liquid state and plastic solid state of soil. Casagrande (1932) developed the first standardized pro- cedure and test device for liquid limit determination. This method, which forms the basis for American Society for Testing and Materials (ASTM) pro- cedure D-4 23-66, consists of placing a remolded cake of soil in the cup of the test device (Figure 2) then cutting a groove down the middle of the cake. The crank of the device is then rotated approximately two revolu- tions per second causing the cup to drop a distance of one centimeter, striking a hard rubber surface with each turn. The liquid limit has been reached when the water content is such that it requires 25 blows of the cup to cause the two halves of the cake to come together over a distance of one- half inch in the groove. This test has developed into one of the standard procedures throughout the world in the soil engineering field. Casagrande (1932) further defines the liquid limit as a measure of the remolded shearing resistance by the following equation: 14 LL = -F log S + C (2) LL - Liquid limit F = Flow index (water content range corresponding to the number of blows in one cycle on the logarithm (number of blows) - water content plot) S = Shearing resistance corresponding to the liquid limit (constant for all soils) C = Constant. Metal trome i\ <53H Operating handle. Front eleyotion «3(pi- Shock obsorbing boss Sectional eleyotion Bross circular dish Co hold specimen Figure 2. Liquid Limit Device In spite of the fact that the liquid limit is also defined as a measure of the dynamic shearing strength of soil at a particular water content (Casagrande, 1958), it has not been determined that a significant relation exists between liquid limit and the original shear strength. The inclusion of liquid limit in this study was based primarily on the fact that it has been shown to be a reasonably good measure of the consistency 15 of a soil (Winslow and Gates, 1963; Skempton, 1944; Rominger and Rutledge, 1952; Seed, et al., 1964a). Thus, at least one term in the equation would account for strength differences in sediments (particularly clays) of varying I textural and chemical composition, e. Plastic Limit The plastic limit defines the lower boundary of the water content range over which a soil will behave in a plastic manner (with liquid limit as the upper bound, see Figure 3). Below the plastic limit the soil acts as a semi-solid and crumbles easily. Due to the empirical nature of the plastic limit, its true nature is not well understood, however, it has been shown to give a general measure of the toughness of a clay (Casagrande, 1932). Plastic limit is quite sensitive to textural and mineralogic changes (Grimm, 1962; Rominger and Rutledge, 1952; Terzaghi, 1955), and was there- fore included as a secondary indication of the sediment consistency. O > "O plastic solid liquid range ~o 'e a> range range PL = Plastic limit LL = Liquid limit SL ■ Shrinkage limit SL PL LL WATER CONTENT ( % ) Figure 3. Consistency Limits (Capper and Cassie ,1960) f. Plasticity Index The Plasticity Index indicates the region over which the sediment behaves plastically (Figure 3), and is defined by the following 16 equation: PI = LL - PL (3) PI - Plasticity index LL = Liquid limit PL = Plastic limit Plasticity index was not utilized in the analysis for the shear strength prediction equation in that it is a combination of two terms already included, It was employed, however, in determining significant correlations among other properties. g. Liquidity Index Liquidity index is expressed by the following ratio which relates the natural water content to the plastic range as defined in Figure 3: tt - WCO - PL LI PI (4) LI = Liquidity Index WCO = Original water content As is evident from equation (4) a liquidity index between zero and one results when the natural water content is less than the liquid limit. The material is thus in the plastic range. Most marine sediments, particularly those near the sediment-water interface, have a liquidity index greater than one, indicating that they exist naturally in a "liquid" state. Rominger and Rutledge (1952) indicate that liquidity index strongly reflects the loading history of soils by effectively canceling the lithologic influence on water content and plasticity index. Liquidity index was also included in the in- vestigation for the purpose of checking interrelationships with other sedi- ment parameters. 17 3. Other Investigations In addition to those parameters analyzed as part of this in- vestigation, other properties have been shown to influence shear strength under specific circumstances. A comprehensive study of the shallow water sediments of St. Andrews Bay, Florida, showed that the ratio of kaolinite to illite clay was one of three major factors determining the variation in shear strength (Holmes and Goodell, 1964). Trask and Rolston (1950) also comment that the type of clay mineral could be one of the main parameters affecting sediment strength. Analysis of the sediments obtained from the Mohole (Guadalupe site) tends to confirm this theory (Moore, 1964). It is apparent from data collected at a variety of locations that the average depositional rate should be considered when estimating the bearing capacity of sediments (Moore, 1964). Shallow coastal regions are generally the areas where the depositional rate exceeds the ability of the sediment to consolidate in a normal manner (Figure 1). Therefore, it is not considered to be of particular importance when dealing with deep sea sediments which are deposited much more slowly in a grain by grain fashion. Calcium carbonate undoubtedly contributes to shear strength as a result of some form of cementation of the individual grains. The exact effect is variable, however both the St. Andrews Bay and Mohole samples displayed a positive correlation between percent CaC0„ and shear strength (Holmes and Goodell, 1964; Moore, 1964). No attempt was made to correlate percent carbonate and shear strength in this report due to the inaccuracy of the limited data available (M. C. Hironaka, personal communication). 18 Finally, the porosity of sediments has been reported to exhibit an inverse relation with shear strength (Moore ,1964) . This is a natural result of a decrease in void volume as the overburden pressure increases, 19 II. REPRODUCIBILITY OF PARAMETERS A. DISCUSSION In order to fulfill the primary objective of this study, the original values of all of the index properties included as terms in the shear strength prediction equation must be reproducible from partially dried sedimentary material. Initial interest in this regard was centered around liquid limit and its correlation to shear strength. Detailed tests were therefore con- ducted to determine to what extent the "original" value could be reproduced after the sediment had been thoroughly air dried. B. LIQUID LIMIT 1. Background Liquid limit has long been recognized as a useful empirical mea- sure of the classification and consistency of soils (Casagrande, 1948). Considerable study has centered around the variables affecting liquid limit, and also the testing and rehydration procedures. Russell and Mickle (1970), and Rominger and Rutledge (1952) have briefly summarized the results of these investigations. The liquid limit of soils is currently determined following ASTM procedure D-423-66, utilizing the Casagrande Liquid Limit device (Casagrande, 1932). The steps necessary for preparation of the sample for this test, as specified in ASTM procedure D-421-58, require a complete air drying and then thorough breaking-up of all aggregations prior to rehydration to the liquid limit. Although the values obtained from terrigenous soils by this method were less than those determined from natural un-dried samples (Casagrande, 1932; Winslow and Gates, 1963), the relative percentage differ- ence was not excessive. Marine sediments present a much different situation, 20 in that they exist in the natural state at water contents far in excess of the liquid limit. For convenience, and in accordance with other methods (Lambe, 1951), many laboratories perform the liquid limit test on marine sediments without going through the drying process, as sufficient desi- ccation may take several days, or even weeks to complete. Liquid limits determined in this manner are thus representative of their in-situ values. Since the majority, if not all, of the values used in this analysis were obtained from undried samples, it was necessary to investigate the effect of a complete air drying on the reproducibility of the original liquid limit. 2. Test Procedures The 20 sediment specimens used in this experiment were obtained from four cores collected in a water depth of approximately 7200 feet at a location 40 miles west of Monterey, California. A gravity corer with a PVC liner and 420 pounds of weight was used to obtain these samples. Immediately after removal from the corer, the liners were capped and placed in a barrel of sea water to prevent desiccation. Within two weeks after collection, the cores were cut apart and tested without drying. The values obtained were thus considered to be valid in-situ or "original" values of liquid limit. After this first test, the samples were placed in open glass containers and allowed to dry at room temperature for a period of approximately four months. The hardened material was then rehydrated with distilled deionized water and allowed to "soak" for 24 to 72 hours. Distilled deionized water was used on the assumption that this represented as closely as possible the water which had evaporated during drying and to avoid any complications which might arise from exchangeable ions. It was theorized that the salts in the original sea water would again redissolve in the distilled water. 21 The excessive rehydration time was employed to assure that the sediment had absorbed as much water as possible. Winslow and Gates (1963) determined that the best results are obtained if a 24 hour rehydration time is used when attempting to reproduce the Atterberg limits of dried soils. Upon completion of rehydration, the soft wet aggregates were broken up and the sediment thoroughly remolded to assure homogeneity prior to conducting the liquid limit test. Upon completion of the second set of tests, the sediment was placed under an exhaust vent and again allowed to air dry. Complete drying in this manner required from one to three days. When the specimens were thor- oughly dry, they were broken up in a motar, as required by ASTM procedure D-421-58, and rehydrated in the same manner as described above. At the end of the rehydration period, each sample was vigorously mixed and then tested for liquid limit. 3. Test Results As was anticipated, after the air drying process, the liquid limits were lower than the values obtained prior to drying. The high percentage reductions involved, on the order of 30% to 40%, were however, totally un- expected (Table I). Casagrande (1932) does note that organic colloids are partially destroyed upon drying, but a reduction in the liquid limit value from this cause is most significant when the material has been oven dried. From the initial liquid and plastic limit values, all specimens analyzed in this experiment plotted below the "A" line on the plasticity chart (Casagrande, 1948), suggesting that they were organic in nature (Figure 4). Casagrande presents data showing a decrease of 28.8%, 26.4%, and 15.9% in the liquid limits of three oven dried samples. Presumably the percent decrease would have been less had the samples been air dried. 22 TABLE I LIQUID LIMIT TEST RESULTS CORE Interval in. Original Liquid Limit Liquid Limit After One Drvine Liquid Limit After Two Drvings CH-2 0-3 130.0 82.0 76.0 12-15 127.0 82.4 77.4 24-27 135.0 85.2 76.2 36-39 128.0 80.8 75.1 48 51 119.0 85.0 74.6 60-63 107.0 78.6 71.2 HH-1 0-3 131.3 87.4 74.9 12-15 128.5 87.6 74.7 24-27 134.3 89.4 79.2 36-39 117.5 85.7 75.1 48-51 117.8 83.8 71.5 NR-1 0-3 126.9 87.3 78.4 12-15 114.3 84.2 75.1 24-27 123.8 84.0 77.1 36-39 119.9 81.8 71.9 48-51 107.5 76.3 73.7 SW-1 0-3 106.8 83.4 78.5 12-15 187.0 87.8 77.1 24-27 65.5 84.5 81.0 36-39 102.5 102.0 74.3 23 • 100 I nor go nic Soil /• X 80 "O *60 (J O o_ 40 • Organic Soil 20 • I • • • I I l I i 80 100 120 140 160 180 Liquid Limit Figure 4. Plasticity Chart for Sediment Samples Used in the Liquid Limit Tests Wins low and Gates (1963) conducted comprehensive tests on drying and rehydration methods for both organic and inorganic soils. They observed virtually no decrease in liquid limits for both types of soil after a 24 hour rehydration period. Two soils which contained montmorillonite clay did exhibit a decrease in liquid limit of 18.57,, and 137„ even after rehydra< tion for 24 hours. It was also noted that up to a 20% reduction in liquid limit can be expected if the rehydration period is less than 30 minutes. As may be seen from Table I, the liquid limits obtained from the second and third tests were distributed over a much narrower range than were the original values. Possibly this may be attributed to the inexperience of the operators who determined the initial values. All subsequent liquid limits (in the second and third series) were performed by more experienced personnel. In remolding the material after the first drying and rehydration it proved easy to break the large wet aggregates apart, but considerable 24 mixing was required to return it to a condition similar to the original smooth consistency. This was not nearly as great a problem in the final group of tests where the dried sediment had been ground to a fine powder prior to adding water. The narrow range of values appears to support the fact that the material was somewhat more homogeneous in the third series of tests. One difficulty with the procedure involving grinding is that liquid limit has a fairly high negative correlation with median grain size. Per- haps this pulverizing of deep sea sediments, which are extremely hard when dried, may result in erroneous values depending on the degree of grinding. Although it is evident from this experiment that the liquid limit deter- mined from a dried marine sediment will be lower than the in-situ value, the degree of this reduction is uncertain. In effect, the liquid limit of oceanic sediments cannot presently be considered to be a reproducible quantity. The multiple correlation coefficient between the second test values and the original liquid limits for three of the four cores (the initial values for the fourth core were erroneous) was .662. It is therefore quite possible that a relation may eventually be developed which will enable the computation of in-situ liquid limits from the combined values of organic content and the liquid limit as determined after the sediment has dried. C. OTHER PARAMETERS 1. Depth in the Core The usual practice when storing sediment cores is to mark the depth intervals on the container itself. If a certain section is removed for testing, a dummy plug is inserted in its place, keeping all material in proper relative position. Therefore, it should be possible to determine the depth interval of a specimen with little difficulty. 25 2. Water Content With the exception of the results of analysis conducted as part of this investigation (Section IV), there is presently no method of reproducing the in-situ water content. An investigation is currently being conducted at the Naval Postgraduate School on a correlation between water content and salt content of marine sediments. If successful it will then be possible to determine the original water content by chemical means. 3. Median Grain Size According to ASTM procedure D-421-58 air dried samples should be broken apart in a mortar prior to grain size analysis. Lambe (1951) specifies that the sample should not be dried, particularly if clay is present, as the individual particles may undergo a change in size or shape. In dealing with marine sediments, satisf.-.ctory reproducible results appear to be obtained if the specimen has not completely dried. If the material has dried, it is presumed best to rehydrate the sediment over a period of several days until it is fluid enough to conduct the mechanical analysis. In this manner there will possibly be little or no damage to the individual grains. Breaking-up in the dry state as specified by ASTM procedure D-421-58 is not recommended for marine sediments. 4. Plastic Limit Since the plastic limit is also affected by the consistency of the soil, it is assumed that it is reproducible to approximately the same degree as is the liquid limit. This assumption is based on only a limited amount of research conducted on this subject (Casagrande, 1932; Winslow and Gates, 1963). 26 III. DATA A. INITIAL REQUIREMENTS AND LIMITATIONS The nature of this study necessitated that the data acquisition be limited to those cores which had been tested for nearly all their engineering parameters. The liquid limit and median grain size were of particular in- terest, hence such data was not useful unless these two properties had been determined. Following these requirements, data relative to approximately 200 cores was obtained from four sources. The majority of this was provided by the Naval Civil Engineering Laboratory in Port Hueneme, California. Addi- tional information was also obtained from technical reports by Richards (1962) and Keller (1964), and from the National Oceanographic Data Center. The following two additional limitations were imposed on this initial data. First, in order to truly represent a deep sea environment, only those cores taken in water deeper than 6000 feet were considered. Although it is recognized that portions of the continental slope may thereby be included, such a depth was selected based on the availability of data and also on the assumption that sediment composition does not vary significantly between 6000 feet and the deeper abyssal plains. Additionally, deep ocean sediments are not apt to be over-consolidated and therefore very few abnormally high shear strength layers will exist to distort the results. Smith (1962) pro- vides a discussion on the merits of classifying various different provinces of the ocean according to water depth. In view of the extremely fine grain size of most deep sea sediments, 0.01 millimeters (Wentworth fine silt) was established as the upper limit of median grain size for each core specimen included in the analysis. Samples having a greater median grain size in- variably contained a high percentage of coarse silt and sand, and were 27 therefore assumed to be non-representative of true deep sea sediments. The above restrictions resulted in 114 cores being included in the final analysis, from which a total of 701 data points were derived. Consider- able effort was required to accumulate this data, and it is probable that it represents the majority, if not all, of the existing deep sea sedi- ment cores in the United States on which a full suite of engineering properties have been evaluated. The actual data for those parameters utilized is tabulated in Appendix I. B. GENERAL Tables II, III and IV and Figure 5 through Figure 9 give geographical position, depth, and other general information about the cores utilized in this study. The exact locations of 33 of these cores was not available, hence only their approximate position is listed. The "Data Points" column refers to the number of intervals in each core that met the initial estab- lished requirements. For ease in data handling and presentation, each core was assigned a reference number. This number is used in identifying the core locations on Figures 5 through 9. The tables also identify the cores ac- cording to their original designation as assigned by the collecting agency. In order to give a more complete picture of the ranges and statistical parameters of each of the engineering properties analyzed, Table V and Fig- ure 10 through Figure 15 were prepared. It will be noted that the plastic limit, plasticity index, and liquidity index were determined on 573 of the samples studied. It is of particular interest that several of the histograms, notably that for water content, approach a normal distribution. The histogram for liquid limit values are evenly distributed, though the histogram is more peaked than 28 normal, and the high concentration of median grain sizes around 9.5 cp is quite apparent. As may be seen in Figure 10, shear strengths of less than 2 90 gm/cm obviously predominate in these cores. 29 TABLE II POSITIONS OF NAVAL CIVIL ENGINEERING LABORATORY CORES Reference Original Data Position Number Designation Depth (FT) Points Longitude Latitude 1 to 18 BS-A Series 9780/13, 300 120 See Fig. 8 19 to 41 BS-B Series 14,150/15,450 197 See Fig. 8 42 to 55 BS-C Series 11,700/19 ,200 60 See Fig. 9 56 C6-C1 8100 8 41°44'N 64°58'W 57 SM-1 6000 6 33°52'N 120°35.8'W 58 SM-2 6000 7 33°52.2'N 120°36.0'W 59 9-1 11,400 7 33°46.8'N 121°50.9'W 60 9-2 11,650 8 33°49.5'N 121°49.9'W 61 9-3 11,700 8 33*48. 9'N 121°51.5'W 62 9-4 11,700 7 33°47.9'N 121°52.4'W 63 10-1 12,100 1 32°00.1'N 120°39.8'W 64 10-2 12,100 7 32°01.1'N 120*38. 8'W 65 10-3 12,200 7 31°58.2'N 120°38.8'W 66 PMR-1 8,700 4 33°49.3'N 121°09.4'W 67 A 17,100 2 N. of Christmas Island* 68 B 18,900 3 Tokalau Trough* 69 C 18,900 2 Tonga Trench* 70 D 14,400 3 S. Fiji Bas in* 71 E 15,900 3 Tasman Abyssal Plain* 72 F 14,400 5 Coral Sea B a sin* 73 FT 14,400 5 Coral Sea* 30 Reference Original Data Position Number Designation Depth (FT) Points Longitude Latitude 74 G 14,700 4 Solomon Basin* 75 H 13,200 6 Solomon Basin* 76 K 10,800 5 W. Timor Sea* 77 LI and LT1 18,600 10 W. of Java Trench* 78 LT2 18,600 5 W of Java Trench* 79 M 21,600 5 Java Trench* 80 N 14,400 8 W. of Sumatra* 82 0 13,800 6 Indian Ocean* 81 OT 13,800 4 Indian Ocean* 83 P and PT 10,500 5 Bay of Bengal* 84 Q and QT 9,600 4 Andaman Basin* *Exact positions for these cores were not available 31 TABLE III POSITIONS OF CORES FROM A TECHNICAL REPORT (Richards, 1962) Reference Original Number Designation 85 D-lp 86 E-46 87 E-47 88 E-48 89 F-6 90 F-10 91 F-ll 92 F-12 93 F-13 94 F-14 95 F-15 96 F-16 Data Position Depth (FT) Points Longitude Latitude 8,400 6,600 6,600 7,200 7,440 8,040 8,040 7,940 7,920 7,850 7,920 7,920 1 4 4 2 13" 4 7 5 3 8 7 3 > 30°N 45°N 42°N 75°W* 57°W* 65°W* *Exact positions for these cores were not available 32 TABLE IV POSITIONS OF NATIONAL OCEANOGRAPHIC DATA GENTER CORES Reference Original Number Designation Data Positions Depth(FT) Points Longitude Latitude 97 31884-2A 14,950 1 16°55'N 179°06'E 98 31884 -4A 18,750 2 llo02'N 179°58'W 99 31884-7A 19,150 1 01°57'N 179*46 fW 100 31884-19A 15,450 1 02°00'N 160°00'W 101 BS-1 12,100 3 24°18'N 86°20'W 102 BS-2 12,100 2 24°25'N 85°39'W 103 BS-3 6,230 4 24°45'N 85°49»W 104 Proj.101 BS-1 8,950 6 28°02'N 87°08'W 105 Proj.101 BS-2 11,100 14 25°09'N 88°51'W 106 Proj.101 BS-3 9,100 9 26°26'N 87*40^ 107 Proj.101 BS-4 12,000 7 23°20'N 93°31fW 108 Proj.101 BS-5 12,500 12 25°02'N 91°03'W 109 AGS -30 BS-1A 11,200 3 28°59'N 70°30'W 110 AGS -30 BS-12 7,200 7 20°20'N 95°14'W 111 AGS-30 BS-13 12,000 7 23°10'N 94°12'W 112 AGS-30 BS-14 8,950 7 23°09'N 96°10'W 113 AGS-30 BS-18 11,600 12 24°42'N 89°34'W 114 AGS-30 BS-19 11,200 10 24°44'N 89°34'W 33 o in O o O o oo CO O in w C o •H *J CO CJ o CD u o c CO CD V o o •H ■U c CO t-t u < m 0) u 3 60 •rt p4 34 — w y o v^ 38 .27 '21 iSsAN FRANCISCO 2.2 .30 12- .31 30 33- .34 35- .36 41- '40 . -37 39 38 /^MONTEREY •3 •2 \ 36 •1 C •4 ,5 -6 / 10- •9 •7 ) •8 / ^34 62.61<60 -66 58-" ^ — 63,64,65 32 •12 -13 18- -11 •14 •15 17- '16 128 I 126 I 1f 122 120 I I Figure 8. East Pacific Core Locations 37 >o ^ » ' Tt * Tf nO • • ■ • • cs 00 • it • in • in in • o < -j o in • in • D i/» Z z U4 Q. - 00 < in in • ■— ■" ~ < X u < 1 o ^~- -«-'—* r~\ w C o « U o ►J *■< o 3 (0 c C - u z LU o LU too 8C - 66, 60 40 20 22 111 96 57 38 30 i2ll 0 20 40 60 80 100 120 140 160 SHEAR STRENGTH ( gm/cm ) 180 Figure 10. Shear Strength Histogram LU U Z LU 3 U U O 100 eo O 60 >- u z LU 3 o LU 40- 20- 93 64 44 19 21 26 ?1 107 109 72 32 28 10 16 10 5 5 20 40 60 80 1O0 120 140 160 180 2CXT 300 400 WATER CONTENT ( % ) Figure 11. Water Content Histogram 40 V z IXJ C£ C£ Z> z IU o UJ 140 - 120 100 - 20 40 60 60 100 120 140 160 180 200 220 LIQUID LIMIT (% ) Figure 12. Liquid Limit Histogram 140 UJ U z UJ on az. Z> U U O o >- u z _> 40 o UJ D^ 20 120 100 80 60 150 68 27 1 _?_ 109 85 53 26 17 ^XJ-ir^L., ,A X 10 20 30 40 50 60 70 60 90 100 110 PLASTIC LIMIT (% ) Figure 13. Plastic Limit Histogram 41 200- nf 160- Lu 140 U z II I oi 120 az. U U 100 o u_ O 80 >- u „ ^ 60 UU O 40 LU LL. 20 200 96 63 52 23 3? 126 84 15 6 7 8 9 10 11 MEDIAN GRAIN SIZE (cp) 3 1_JL 12 Figure 14. Median Grain Size Histogram LLI 140- U Z £ 120|- => y ioo- o u. o 80 > LU O 40 LU 152 90 ?e 124 66 26 QLdffl. '12 4 6 8 10 10 SENSITIVITY Figure 15. Sensitivity Histogram 42 IV. STATISTICAL ANALYSIS A. METHOD 1. Regression Analysis Stepwise multiple linear regression was employed in the determina- tion of both the final shear strength prediction equation and significant correlations between other engineering parameters. The Naval Postgraduate School IBM-360 FORTRAN library program BMD02R was used for this analysis. This is one of the Bio-medical series regression programs developed by the University of California, Berkeley (Dixon, 1970). Stepwise multiple re- gression was selected in that none of the variables examined were considered to be completely independent of the other engineering properties. Utilizing this procedure, the data is analyzed to determine which parameter explains the greatest portion of the variability in the dependent variable. The program continues in steps, successively selecting the next most important variable to be added to the regression equation until all the variables which meet specified requirements have been included. The term chosen in the final step thus explains the least percentage of the variability. Holmes and Goodell (1964) present a discussion on the merits and limitations of applying regression techniques to natural sediment systems. In the analysis which follows, R is defined as the multiple correlation coefficient, That portion of the variance of the dependent variable which is accounted for by the estimated linear regression on the independent variables is de- noted by RSQ (Hays and Winkler, 1970). 2. Confidence Limits ■ ii » . .-i ■■ * Limits for the 957» confidence level have been drawn on the shear strength and water content plots (Figure 16 and Figure 18). These limits 43 indicate the approximate accuracy of the predicting equations. If all computed values were exactly equal to the true values, every point would fall bn the 45° line, and hence the confidence limits would have no meaning. Where a scatter of data exists, however, the confidence limits de- fine the percentage of points which fall both within, and without, the parti- cular bounds. For the 957» level, 5% of the points will fall somewhere outside the confidence limits. In utilizing the respective equation, it can be assumed that there is a 957o probability the computed value will be within the limit bounds. B. STATISTICAL RESULTS 1 . Shear Strength and Vater Content Equations Approximately 60 separate regression analyses were conducted to establish the optimum shear strength prediction equation. With the excep- tion of median grain size, which proved too insignificant for inclusion, correlation coefficients between each parameter and shear strength were highest when the logarithm of shear strength was used as the dependent variable (Table VI). The column titled "Equation Multiple Correlation Co- efficient" in Table VI refers to the coefficient obtained when the four most significant variables were included in the respective shear strength regression equation. When the natural value of shear strength was used as the dependent variable, liquidity index replaced liquid limit in the equa- tion. It is of interest to note that liquid limit did not prove particularly significant in any equation unless water content was included as one of the parameters. The equation derived which explains the maximum variation of shear strength is as follows: Log(SS) = 1.866 + 0.0023(LL) - 0.597(1/D*3) - 0. 00454 (WCO) + 0.00672(PL) (5) 44 TABLE VI SHEAR STRENGTH CORRELATION COEFFICIENTS DEPENDENT VARIABLE INDEPENDENT VARIABLES MR WC LL PL D DM cp PI LI Shear Strength (gm/cm2) -.318 -.119 -.080 .259 -.298 -.215 -.106 -.266 .506 Logarithm (Shear Strength) -.374 -.177 -.139 .312 -.3/5 -.175 -.140 -.267 .558 WC = Water Content (%) LL = Liquid Limit (7«) PL = Plastic Limit (%) D = Depth in the core (cm) DM - 1/D*3 cp = Median Grain Size (cp units) PI = Plasticity Index LI = Liquidity Index MR = Equation Multiple Correlation Coefficient 45 SS ■ Shear strength (gm/cm ) LL - Liquid limit (%) D = Depth in the core (cm) WCO = Original water content (%) PL = Plastic limit (%) True versus computed values (using equation 5) of shear strength are plotted in Figure 16. Though the 957« confidence limits are a bit wide, additional data will undoubtedly reduce the variability. The depth term in equation (5) differs considerably from the linear relation reported by Arrhenius (1952), Bjerrum (1954), Richards (1961), Moore (1964), and others. The non-linear manner in which sediment compacts, suggests that a depth-shear strength relationship is also probably non- linear. An extensive amount of numerical analysis was therefore conducted to determine the highest correlation between the two parameters. In every comparison with logarithmic or natural values of shear strength, the term .3 1/D" proved to have the greatest correlation coefficient (Table VII). When this term was included in a multiple regression, the significance (increase in RSQ) of the linear depth term decreased to nearly zero. TABLE VII CORRELATION COEFFICIENTS FOR DEPTH IN THE CORE Shear Strength Relation D 1/D"3 D + 1/D*3 Shear Strength (gm/cm2) .276 -.282 .299* Logarithm (Shear Strength) .313 -.343 .354* *Multiple correlation coefficient 46 to d 0) H vO a u o 60 In ( un/wB ) ij46u9J45 jdoijs p94ndaio3 c 47 As noted previously, the depth term exhibited a higher correlation coefficient when compared with the logarithm of shear strength. Computed strength, utilizing the most significant depth relationship, and actual strength for a typical core are plotted in Figure 17, together with data from Arrenhenius (1952) and Richards (1961). It should be noted that the 3 1/D" term exerts a measurable influence on the strength-depth relation- ship to a depth of only approximately 60 centimeters. This is the portion of a sediment column which is undergoing the greatest amount of consolida- tion, and as expected the increase in strength exceeds a linear rate. Be- low this depth, the rate of increase is essentially linear, as observed by Arrhenius (Figure 17). It was also very interesting to note the similarity between the linear shear strength - depth relationship developed by Arrhenius (1952) and that calculated in this study. The two equations are respectively SS = 55.0 + 0. 00143 (D) (6) SS = 36.2 + 0.00142(D) (7) 2 SS = Shear strength (gm/cm ) D = Depth (cm) Though the slopes of the two relationships are virtually identical, the reason for the difference in the constant terms is not evident. Original water content values were utilized in the derivation of equa- tion (5). Though this is presently not a reproducible quantity, the true values were included in the first analysis on the assumption that it may eventually be possible to determine the original water content of dried marine sediments by chemical means (Section II. C. 2). To solve the immediate problem of determining a value of water content to be employed in equation (5), a second regression analysis was conducted to establish correlations 48 10 20 30 40 50- SHEAR STRENGTH (gm/cm .) 25 50 75 I I I I Average Strength Profile (Arrhenius,l952) Typical Core Profile Richards (I96I) £ 60 a: O 70 U z 80 x £ 90 a 100 120 130 140 150 160- Figure 17. 100 I I I I Strength Profile ~ Defined by (D + l/D ) True and Computed Shear Strengths vs. Depth in the Core 49 between water content and the other properties. Results of this analysis indicate that water content itself may be predicted with a farily high degree of accuracy (multiple correlation coefficient = .881) on the assumption that liquid limit, plastic limit and median grain size are reproducible quantities. Utilizing the available data, the water content prediction equation is: UCC = 0.689 (LL) + 1.648 (PL) - 0.0752(D) + 7.74 (cp) - 67.65 (8) WCC = Computed water content (7„) LL = Liquid limit (%) D = Depth in the core (cm) cp = Median grain size (phi units) PL = Plastic Limit (%) The grain size and depth terms of equation (8) account for slightly over three percent of the total variability of water content. Since grain size analysis is a time consuming laboratory process, this term may be ignored with but little loss in accuracy. The resulting equation then takes the form: WCC = 0.927(LL) + 1.336(PL) - 0.0718(D) - 7.742 (9) This equation accounts for slightly over 757» of the variability of water content (Figure 18) . In order to give a more valid picture of the predictability of the value of shear strength, the shear strength regression was re-run with equation (8) substituted for water content in equation (5). Although the overall significance of the equation was reduced by seven percent, it was still considerably higher than if no water content term were included. 50 o CN C C4. O r> CN O -*- o C T3 CN o 0) V 4J 3 Urn a 0) c 4— O (0 T" o a) CN 3 T- o o oo u 60 •H |U84UO^ .1940/^ psjndiucQ 51 2. Other Correlations In the process of analysis of the data, several additional in- teresting relationships between the sediment parameters were investigated. a. Liquidity Index - Logarithm Sensitivity Bjerrum (1954) briefly discusses a relationship between the logarithm of sensitivity and the liquidity index of Norwegian marine clays. Richards (1962) presents similar results for various Atlantic Ocean sediments, In the case of the first of these studies, the material investigated (while marine in origin) had been uplifted and was no longer in its original satur- ated condition. The data of Richards is too sparse to establish a reliable relationship. A regression analysis was therefore conducted on the data from 509 samples (representing all of the samples for which sensitivity values were available), to see if sensitivity was determinable from liquid- ity index. The regression initially proved to be insignificant, until as suggested !• . Richards, the regression line was forced through the origin (Figure 19). The correlation coefficient then increased substantially, and the slope of the regression line proved to be virtually identical to the average of the lines determined by Richards (1962) from data obtained in 2 his areas E and F in the North Atlantic Ocean. The usefulness of this relationship lies in the fact that if the origin- al water content, liquid limit, and plastic limit of a sediment sample can be measured, equations (3) and (4) and the regression line from Figure (9) may be used to obtain the sensitivity. It is realized that these results Ratio of true to remolded shear strength. 2 The majority of Richard's data used in this study were from areas E and F. 52 CO a, Si W + + + in X » > 4J •H W a Cv> w CO 3 to > CO )■ 3 00 53 may be somewhat oversimplified and that the true correlation between the two elements might vary for different broad depositional regions. If these various relations can be identified when more data becomes available, it may well be possible to collect disturbed samples, measure the remolded strength, and thereby obtain values of the original shear strength by multi- plying the remolded strength by the sensitivity obtained from a plot similar to Figure 19. Shear strengths for the available data were computed in this manner and subjected to a regression on the true shear strengths, with a resulting correlation coefficient of .725 (RSQ = .525). Although this translates to about a 20% increase in explanation of the variability of shear strength over equation (5) , it should be realized that the true remolded strength must be measured and therefore the procedure is not applicable for use on material which har dried below its natural water content. Strangely enough, when the results of equation (8) were substituted for the original water content in calculating liquidity index, the computed - true shear strength correlation coefficient was exactly the same as that indicated above, and the values of computed shear strength were identical to three significant figures in most cases. The 95% confidence limits using this method were 2 nearly 10 gm/cm closer to the regression line than those of Figure 16. b. Liquid Limit - Water Contei.t Of considerable interest in this investigation was the high correlation (.802) existing between water content and liquid limit. The constant term in the equation for the regression line proved to be relatively unimportant, and therefore the line was forced through the origin, with virtually no decrease in the correlation coefficient (Fig- ure 20). The equation for this relationship is: WC - 1.352(LL) (10) 54 320 2801- 240h c C o U i— 0) -*— D 200,— 120 Liquid Limit Figure 20. Water Content versus Liquid Limit Relationship 55 One possible explanation for this correlation is possibly that fully saturated marine sediments exist in a narrow range of water contents at some fairly constant percentage above the liquid limit. If true, this would mean that the water content is determined to some degree by the same factors which act to control liquid limit, and vice versa. This theory is supported by the fact that liquid limit and water content have similar correlation coefficients with plastic limit, median grain size, and plasti- city index (Table VIII). As may be noted in the table, liquid limit was completely independent of depth in the core, whereas water content and depth are inversely related. 56 TABLE VIII WATER CONTENT AND LIQUID LIMIT CORREiATION COEFFICIENTS WITH OTHER PARAMETERS PARAMETER WC LL PL D l/D-3 cp PI LI Water Content - .802 .773 -.141 .178 .316 .501 .444 Liquid Limit .802 - .669 .013 .052 .416 .832 -.039 WC - W;?ter Content LL = Liquid Limit D = Depth in the core cp = Median grain size (cp units) ?I = Plasticity index PL - Plastic limit LI = Liquidity index 57 V. CONCLUSIONS AND RECOMMENDATIONS A. CONCLUSIONS The results of this data review and analysis indicate that several conclusions of interest can be drawn: 1. The liquid limit of marine sediments is not a reproducible quantity by present techniques. 2. Utilizing equation (5), the shear strength of deep sea sedi- 2 ments may be estimated to an accuracy of + 40 gra/cm at the 957o level of significance. This equation will undoubtedly be improved as additional data becomes available. 3. Original values of water content can be determined with a fairly high degree of accuracy utilizing equation (8) or (9). 4. The water content of the sedi-.' ents investigated was highly dependent on the value of liquid limit. 5. The liquidity index - logarithm sensitivity relation observed by Richards (1962) r=nd Bjerrum (1954) appears to be valid. B. RECOMMENDATIONS 1. Extensive use of the Casagrande liquid limit device indicates that a revision of this test is necessary for application to marine sedi- ments. Not only does the device and the type of tool used result in variable readings, but * the dependence on the operator is entirely too great for useful engineering determinations. ASTM Special Technical Publication 254 (I960) contains several excellent recc. unendations for revision of this test. 58 2. As a result of their naturally saturated &£ate and the physical changes which occur upon drying, a question arises as to the validity of ASTr-1 procedure D-421-58 when applied to saturated samples obtained in oceanic coring. A review of all soil tests affected by procedure D-421- 58 (when applied to marine sediments) is considered a necessity to deter- mine the effects of drying. 3. Serious doubt exists regarding the reproducibility of plastic limit and median grain size of fine grain oceanic sedimer. t:s once the material has dried. Therefore, it is recommended that further studies be made in this area. 4. The apparent depen ' nee of liquid limit on organic content, indicates that further research is warranted in an effort to correlate these two parameters. 59 APPENDIX A DATA ANALYZED The majority of the data analyzed is included in this appendix. Data from 17 of the cores (accounting for 84 data points) was loaned for this study, however, it was not released for publication by the collecting agency. The following abbreviations are used in the tabulations: Ref. No Reference Number (Tables II, III, and IV) SS Shear Strength gm grams cm centimeters WC Water Content LL Liquid Limit PL Plastic Limit MGS Median Grain Size PHI ....... Median grain size in Wentworth phi units mm Median grain size in millimeters PI Plasticity Index LI Liquidity Index SENS Sep ;tivity 60 CO z w CO t-t ►J r-l ex, co O 1—1 o 00 m V* CM 00 CM CM CM ffi co CO a> C\ o vO CM o> m m CO vO » O m Is- m rH OV m in 00 in co CO F-* ►J CT> oo oo CO 00 l-i cr> o r^» r-l O o CO r-5 r-l r-l r-l r-4 1—1 /-v 5^ vO LO m m — • vO m vO vO r~» m 1—1 CO fx r-l O r*» o CM o tH CM i-i O <-* r~l sc i-4 r-l r-l r-l i—i 1—1 1-1 r-l i—l i—l i-H i—i t-* •-s CM e o 1 cr> m m CM CO CTi CM r-l CM CM vO cr» CM m CO vO ON CO vo o> o ^ i-t r-t m • cu o r-l CM CO mi z: 61 oo 55 W in M rJ M P-. en on ON m T-( oo S^ s-' hJ f»< ON o i—i ON en NO rH - 00 o o CM vO O O 00 en en o r^ - r^- m vO CM 00 t-l VO O rH vO vO rH vO rH vO N-^ 1—1 CM rH i—l r-l CM CM en en CM CM » 4-> /-^ o- e co - r*. 00 CM CM CM vO CO r^ CO m O O o o o O g o o o o O O o o o O O o o o O o o o o O O o o o O o o o o o CO O X on t-I r-< r-l ON M CM CM CM CM vD r^ ON On On 00 CM CM CM o r-t O r-l o t—i ON r-t r-t r-l r-l t— 1 r-l r-l t-t r-l /"■N *4 >^> ►-5 CM m m oo LO m \0 ON VO m s N^ o vO ON m CO m m >>• CM on en <. CO . t^ CO o cn vO o-* CM m co vO ON CM m 00 t— i -* Q ^ r-l r-l r-l r-l t-i CM CM 1+^ . ; M ►J r-4 CM CO <* E-S v-^ ►4 CM r"\ r>» 00 On o ON ON 00 On ON On o> CO ON •"». is? 0^ 5 o r-. o vO m CM m CM m O i-^ m «^x oo CM CM o vO m m r^ m O r-l m o t-i 1-1 CM r-l f-l 1—1 t— 1 r-l i— 1 i— i t—i r-l r-l rH rH •-S CM E O I i-H o r-» T-l CO r^ CM 00 Ox 00 vO 00 - vO vO ex r-l >.• r-l O CM CM CM ex. vO co r-l CX CO ex. r-i 00 on ON CO on f-i r-H t— 1 ON on CM l-l ON CM r-l ON ON m r-l <}• <* m co en CM r^ CM m en r-l 1^. o m i-l r^ ON ON cy. On ctn C> ON on »• on i-i o r-< o CM m CO ON /— \ CM E o o ^ CO on CO \D CM r-l m CM vO !-t co vo r>. r^ en ON vD • CM i CM — * en r-«- t~» «tf m v£> r^» \D m r^ CM en CM r-« CM r-» i— i co en 00 en r-» CM r-- CM t vO in 0^ r^ 00 in st s0 r- vO r- 00 r- CO a:> CT CM o in o CM r- in ON CO ■vt r-l r-l in i— i 1—4 I— I NO o CO m CM i—i I-l O r-4 l-H o o r-4 o O o O c O O o O o O o O o O o o o o O o o o O i O O o O o O O o o o o o o o O o o o o CO O O o o o o o o o o o o o o c o o o o o X CT> on on CO o> m ON o\ CM r-4 r- r- CM r-4 ON i-v CM on M »• • • • • • • * • • « » o CO ON On i— I ON o on 00 00 CO CO 00 co 00 CO vt o O CM CM r~ co o r-4 (0 ►J CO h- O i—4 o o i—i r-4 CM CM hJ r-4 r-4 r-4 r-4 i—l r-l r-l m r>- 00 Vt CO NO i—i t r-l NO rH <4- CM vt vf vt fO ^~v CM E CM O m o in 00 00 ««»' CO m CM CO r^ :^. CO O vt o^ CO o* vj- O' vt o a> u co vO c< CM in 00 r-4 -* CM CM U-J 00 ON o CO M 0 m t CO co p- sO «tf P- »-l t— 1 ^-» t— 1 • — » 1 — 1 *— 1 1— ( r-H r— 1 1— i t-* vD cr CO in 1— 1 r-H r- M • • • • • 04 co tH 0 ro p- CO rH CO r-A cr- p- .— 1 0> 1— ( a: CM t cr r* CM Oh • • • • • 00000 O O O O 0 O r-t i-H 1— ' <—l •— * ••"s C O >t O >4" P- xO co >0 0 cr r-( r- CM s-^ ■-« co 0 in 00 CM vO m

O cr 00 tJ t — T r— 4 • — 1 t— < 1—1 1— t /-s s~s vO m vO -4- sr O in CO 0 r— 1 O ^^ p-- i-H CO r-l CM •4" CO CM r-{ 1*- CO CM CO -4" «*■ <4" CNJ . 0^ p* CM CO CO CO vO O P- in CM i • • • • • in co 0 r- in CO P- vO co t-H 0 •4- co >fr M- <4 in CM CM CO in CO CO CO x: co 0 co in or a? O CO in CO 0 4J «-v • • • * • t • • • • • Q- E 4) O co cr -4- cr -4- CO cr- o t-4 ro <$■ 0 CO 14-1 j- U> Is- r-l ^0 CM (M CM CM CM (M CM CT CM r-l m >*■ o 4- in cr CO c ex. CM o CM CM in in o oo CM r- -* so Is- m o in in O r- v0 — i o .-H o O O O o c o o o o o o o o O o o o o o o o o o o o o o o o o o o o o o e'- er CM r-l cr CM r-l CT ro ex; CM er cr r-H r- cr a- cr O cr cr O'- cr 00 cr CM CT co cr r- CM i— i o o o o in oo o o o o o (^ cr cm 4" CO r-H cr cr in O Cr s0 co so in in ro rJ p. r-1 cr CM CO CM v0 CM M3 cr r-H in rH CM <$- co 4" •4- in MO o 00 CO 4- vO o C O vO $- o cc in cr in O in O 4- CM r- <4J i— I Lf^ r- oo co o ro co ro cr ^ 4- r-l ro o CD O CO • CM CM 70 to CO o Is- vO CO *D ro o Is- cr o <4- K Cr z M CM <*■ ro ro ro vfr >* «fr ro ro in in in ro OJ ** CO O ro O >fr oo I—I in in Is- 0^ ■-I Is- M in st ro ro I'- r- Is- r-l sr i-H t O m in i—i O M (X. ro o in «t o Is- t r— 1 ro r- in in in O Is- IT ^t -fr r~- o r- Is- in ro in -4- ro in 00 ro o CM sO ro CM ro r^ vO vO i-( .-i i-H i-H CO ro vO i—i r-t r-l i—i •—I CM CM g O o o o O O O o o O C o O O E o O o o O o O o o O O o O O CO o o o o o O o O o o o o o O O X cr o cr C\J Is- Cr .• •J Ph v£> «fr O 4" CO cr o r-H i— 4 ■-( r-l l-< r-i i-H i—l i-H r-l r-J i-l <^\ CSI £ o CO r- «f ro t— ( J CM o -4" i—i CM 00 <^ 00 CM CM * in Sf •4 st- ^0 CO vO «4 t~* o vj" rH r» Is- 0^ n0 o co vO CO >-t «4 -* ■—I r-< r~K r-i 1—1 O O CO r-l CM Sf rH rH rH & >-* vO r~ o^ CM o t~ CM o> in sf 0^ rH Pm S3 CO CO O vO CM CO sf in Is- CO vO co co in •4- •4- SO CM so sf CM in in SO in Sf sf CO in S3 Is- sO in in CM CO CM i— i r-l in CM CO co rH i— i cm co sf o r-l sf rH rH r-l r-l o rH i—i rH r-l r-l rH rH r-K rH c o o o o O o o o O O O O o o o O o O O o O O £ o o o o o o o o O o O O o o o O o o o o O O CO o o 1— 1 o c o o r-l o o- o O o r-l O O o CM o r-l o o^ o o CO o CO O" o rH o o M m CM t cr in Is- sf CO ^-4 r- in r- CO CO CO r~ m in Pi 0> o co 00 Is- r- 0^ r- O 0^ O 0s o rH c^ 0> o> o cr 0^ o> a- 0s r~ st o rH vO r- in st CO in n0 co r- nO 0^ CO CO CM in CO CM Is- s— ' ►J PM 1— 1 Is- o St CM rH o 3- o CO rH CO o o CM CO o o CM in st co CM CO in o rH <—{ CO O st CO >o sf o ro Is- >T o CM t~i 0> s0 o vO r-l r-i rH CM o Is- vO CM o rn >4 in CM w-t iH CM CM CO o -* rH CM CO CO CO St" in sD St st CC) CO CO rH -C cc. o co in CO O CM tn h- o CM co o m in co O CM in Is- O CMI JJ /-V Cl E co 0 Sf C* sf o in o in r-l O CO o -* CM vt in r-i rH r-l rH rH rH w-\ rH Ref. No. vO CM CM 72 tO r\i f— i 00 o o ro CO in Nt" 1-4 v0 o o vt O < v* i—l o st • in <4 Nt cm r- vO vO r-l m >o CM ro vf vfr i—i CO Is- 00 v0 r- in CO M <-J CM r-l t— 1 CM CM CM l—l r-l r-l i-4 r-4 (NJ CM rH r-l 1—1 1-1 CM 1— 1 h- i— 1 r- O in j- ro o co vO O -t ro 0s- o- CM n0 CO i—i CM i-i O ITi r-4 ro CM r-l r-4 V* r-l r-l r-4 •—I r-l r-l ro r-l r-l r-l i—i r- sO c o o O o O o o o O o O O o O O O o o o £ o o O o o o o o o o O o o o o o • o t o • o • CO o o o O o o o o o o o o o o o o o o o o ro 1— 1 r- h- on r- «*■ tT CT- -r ON i-H rM Qn CO 1—1 CO o Is- M prl co (\J r- 0' in r- o >* in o vt Is- r— 1 ir\ 00 Is- oo 1—1 CM cu o> CO 00 0s- 0* r- o o 0s- o a- O CO on 0> o ON Is- Is- ^v !*• <\) in o CM vO »-( in in r^ r-l CM »t CO r- n0 r-l CO vO 00 n^ h- o CM t— l in CO Is- CO 00 O o •4- t— 1 00 Is- vO Is- 00 O ►J (O ro ro in •4- CO m sf CO CO CO CO ro CM co CO ■ ro rM CO /-N er> vO r- 00 r-l in 00 CM o r- in vO ro -4- in 1—1 in r-4 CO in CM >4" i-i CM m CM co CO r-4 co in in rH Nfr «fr CM CM o ^-\ CM E 1 CO CM CM r-l CO r-l CM in -t r- CT s0 o CM r-4 -t in CM CO CO r-4 vO 00 o O CO O CM O- IT, in in O CO vO on CC CM CNJ CM CM r— 1 v^- in in O in CO CM r-l i—i CM CM to to x: CO O ro 00 o CO in 00 o ro in CO o CO in CO CO O co 4J ,— v a e ro O vT co o> t ON -t ro O^ VT o u r-l co r— 1 co vT i— i ro >r r-4 CO *r n0 1-1 0T xM CO ON o r-l CM t CX CM r- r- in r— 1 vO o z w cm t in r-A r-l CO sf r- vO in r- * O sO CO CM- o CO CO o in i-i (M t— 1 i— 1 o CO r-l O i— i r-l r-l p O O o o o O O o o O o £ O o o o o o O o o o o • • • • • • • • » • • CO o o o o o o o o o o o o X 1—1 1— « r- ct> 0^ ■tf r- CT o r- o 33 r- h- 0> CM CM o o CM in o CO P-i 0^ co O O O vO O O o o o 1 ..■ ■-I r-t /~v s^ ^ vC CM n0 vO in o O CO CO CO **-' • * • • • • t • • • • o in r-l 1- CO tf CM v£> CM CO r^ co CM CO CM CM C\] co CO CO CO CM /~\ CO r-l CO h- >t O vO sO CO c CM N-^ o ro CM -4" o O in CO r-l o r-l -3 CO in m vO r~ in co CO co h- r- /""\ s^ r-l CO r-l CO ^0 i— i t> CM in r- o ^^ o s cm .— i O in 4- CM vO t-i vO o in in CT CO o CM CO CM CM r-t rH o r-l r-l t-l r-l r-l f-H t-l r-t /-s CM E • U 00 in O CO vO O n0 sO & Cr- CM i— i vO CM CO O CM r- o in CM t—l i— i i-< CO CM CO S}- CM CO CO , a e en C7^ >3- a £> CO 0^ r-l CM r-l in t—i t*-* • CO J rM i—l CM CM CM r- r-4 Ph o o o o o o o O o O 0^ & O r-4 1— 1 r-l r-4 i-H i— 1 i— l i—i r~l •-4 /— s o r\J i— i f- CM F-l CO sj" 0 CO ro in r-i ^ in CO ro in » r- o Ph to ro ro ro ro ro ro CO ro ro CM CM CO CO <|- »t O O cr in ^ O CO O vO r-4 v-** r\j r-4 <1- tn ro CO o o vO co co CM vO i-3 ►J CO o 00 co CO CO co CO 00 CO CO CO cc x-s ^0 cm (\J r- i— i >* 00 O C7^ O NO sr in o o in r- o <\j <* r-4 ro O ro o -4- ro o 5 i— i CM CM CM r-4 CM CM r-4 CM CM r-4 1-4 f-l ^*\ • CM E u 1 4" ro ■4" ■4" in CO •4- •+ CM >*• r-4 o CO CO o r- o t— i ro o o H ro CO •4- ro CM ro CM vf vt- in in in in CO CO CO o ro in oo o CM in r- o CM •4- o in o m i— i f CNJ OO O CO 00 0"' o o o o o o o o o r-\ CT- vt r-< O <-* o o o o o o o o o i-l CO CNJ CNJ 00 i-t CT CT> O CT CNj o o o cr cr o vt CNJ £ CO cr cr oo in o in t co in o CM E U 1 CO to in CN) CT <-< CT O ro in o cr cr cm ro mo >o cr r*- H rl N N (*1 xf Is- ro >t r-< 0s CO fH 00 Is- CNJ CNJ CNJ CNJ CO --t H CT CNJ in Nt CO in v0 co r- i—i vO l*- o r- CO Is- rH oc z w ro >t r- ro O o cr o O c o 0^ o O O cr cr cr o O o i-H rH r-l r-l rH i—i i—i rH rH rH /-s 8-5 ir\ cr «* «fr CO r- o CO r-l cr r*- CNJ CNJ <}■ o> in CO vt r- CO v^ i-3 ro £> O Is- in Vx* g cr t vS- r<"i IT. ro CO O ro CNJ CO rH i— < rH rH rH r-l r-l rH i—l rH 1—1 r-4 i-i rH rH rH rH |H rH /-s CM E y 1 4 o rH in r- i—l CNJ r-l in CO o (NJ r-i vT CO CO CO cnj OC co rH ^C 0s in rH h- O CO cc oc o LO CNJ in in UN 1—1 v* ro in C\J ro in rH CNJ t— i CO CNJ CNJ I—l lf^ ro ro CNJ CNJ t CO CO Is- in C\l CM N* CO nO r- r- ^ rn Is- CM in O «* O in ►J vO co o cm in o Is- o CM rH t in 00 0^ o * *»• • • t • • • • • • • • • J P* f> CO o st- >t t m o o ro ro ro ro ro CO C\J CO CO CM ro ro t-t a r- CO >*• Is- CM <4" CM in in o V^ CO rH Is- C\J n0 CO Q" O in o CM •* rJ CT- O 00 i— i o o CO o rH o o o •J i-* 1— t rH rH rH rH /"-v J-? O* ro rH i-< rH in in rH r-> Is- CO >t v^ O > v0 CO vO i— < «* rH CM >J" rH sO CO ro ro ro CM CO vT sf ro o CO o CM CM rH rH rH rH rH rH rH rH r-t rH rH rH /~\ CSI e 1 Is- vO o CC -C r-i CM O o- ro o Is- o CO in CM IT, CM CO h- O ro CM 00 . ro (\l r-l ^ CO CM rH O f- ro CO St- CO rH CO " .c CO o CO in CO O CM in r~ o CM «t U x-s ro 0 4- in sl- vT <* t •4" •4" 1—1 in ►H i— t i—i i—i ■—I r-l r-l i—i ■—I i—i r— 1 rH rH rH i—i 00 i— i -o ro rN! in r- vO r-i I—I cr ro Is- r- M Pv, cr rH o in (X; Is- <*■ CNJ ro O CO o 1*- ^4- in nC in vO LO in o vO »o vO in in v0 in cr o cr CT cr oc ro CO 00 cr cr o- cr cr o I—I o o C o i—i o O O o o o o g o o c o o o o o O o O o o o E o o o o o o o o o o O o o o CO o o o o o o o o o o o o o o o S . M EG C\J Is- cnj CNJ t o O 5 i-< rH rH rH r— 1 t\J CNJ r-l rH i— i rH rH rH rH i— 1 rH l-t r-l rH r-H r-l r-l rH i— 1 rH rH I— 1 r~\ CVJ E o 1 in ro> CO (V 00 cr C\J CNJ l—l o in >t ro cr c in vO r- 00 in CNJ O m *4" o in CO cr >i- in in m in r o in o m r—l vO rH sO r~M Q ^ o r-l ro «4- sO CO cr rH CM "4" IT, r- CO O CNJ U--I . CD o vt CtJ ?5 . 79 CO vf 1—1 O r- CM Is- CM (M vO vO 0^ o CM r~ 00 . co v0 CM o z co CO in IT in m m co ^J• <*- CM vO in O sD o <> vf m in Is- o v£ ir\ or, vt (M. >t en LP. o r- o a- & 00 Is- in O cc oc CJ> co U'i Is- rH vO O 00 rH o o o o o o i—i o O o o o O co vt ■S o sO CO o CM CO 00 CO in in o co rH 00 Is- >t co o ^- \_^ c • •J Ah CD CM r-4 a O o o o o o o CM CM E o 1 in 00 CM in CM & >o r-4 CO CM v0 0- vO CO CO CM %o r- vO •h >t in o CO <)• a CM c o- CO 0 CO (M CO r- CO cv CM in o in >o CO CO *t *fr t J r~ o CO o CO 00 O •C 4J ^-s CD O CO c< NT o vf O ir\ a m r-4 vQ rH vO rH CI cr- vt CO O o s-- rH co -j- o CO CT r-4 CM t CO •4- CM CO m >t sj- m ro CO ro ro rO vt CO O CD vO s0 in CM Is- r\j CO o o o in vd- CO sO «t o J Is- Is- ro in Is- nO 00 CO 00 CM ■«t in o cc K P-i oo CO CO 00 CO Is- Is- Is- Is- Is- Is- Is- Is- Is- vO oo Is- Is- r- O cr o o <— 1 CM cc ■* m cr o in Is- r> 00 J- co n0 >r m, CM ro r— ) CO CM • CM •-s 00 CT CT Is- 1—4 Is- vO CM m i—l in 00 co Is- CM st Cr 00 w^ 00 CO O Is- in CO O a CO o r- CO Is- 0- CM o cr CO CM ro Is- Is- * «4- ro Is- Is- cr m in co v£> Is- cr Is- o in in r- o to r-l to x: CO o ro in CO o CM in CO O CM CO O CO m oo o CM in Is- 4J ^-v a e co cr r o 00 t* i—i i— i o cc cr r-l CO -r vO 00 a> r-H 1-4 CM i—i U-t 0^ in o CNJ in CO a* CNJ CO O o o CO 1—1 M 0 vO m i— i CNI r-l r— 1 in *■ in r— 1 o r-l in CO in >r i—i CNJ -3 o r-l r-l r-l r-l r-l r— 1 r-l r-l r-l i— 1 r-< r-l r-l r-l r— i r-l i—i 1—1 CO CO Is- o CO r— 1 o- CO CO co vO r-t o vt CNJ CO CO st CNJ r-l Ph cr CO c CNJ CNJ 00 in CO 0s- CO a CNJ sf CNJ sO -o- 00 o in ip. CO m CO CO m CNJ co CO CO CO co co CO CO CNl r-< CO CNJ O r-l r-l vO o o vO i-i CNJ CO r-l o r> o CO o 00 Is- in vO x0 CO Is- vO 00 CO in in CT O V0 vO CNJ CO 00 . CNJ o rX[ Is- Is- v0 Is- Is- v0 sO Is- Is- Is- Is- co Is- Is- CO o sO Is- r- 6^ co Is- CO &■ •4- r-l r— 1 CO co O o a* rH co Is- CO CNI o v0 N-i' ►J o o r- 1 in Is- O CO m v0 o 00 CNJ >4" Is- CO * CO cr- Is- rH in LP O o- CNI CO 0s- Is- o CO in o Is- in 00 o o o 00 Is- vO ►J t— ( 00 Is- Is- o in in 00 CO 00 Is- n0 o Is- vC in m CNJ i— i v0 CNJ 00 sO CNI 00 o 0s CO 00 s0 a o Is- CO CO CO a> m vt Is- oo ^0 Is- CO r-1 r-l to JZ o en in CO o cnj in CO in co o CNJ in Is- o CNI 00 o CNI U /-^ a g 0 ^r 0s sT o IT\ o v}" 0 sf o in c m r-4 in vt o in l-l co »fr s0 co o r— 1 co v4" vO CO cr rM CNJ Vf cr sO 00 C f-H r-l r-4 r-l . U-l . CO a> o r-l r-iLOvOm rococMroc\jrorococ\ir\j CO sO in eg sj- en vO ro ro ro vO >t CO Is- CNJ in f-i ro o o cr in in O cr o ro in co O O Nfr Is- Is- ro ro Is- ro co in in co o in in cr nO >t o cr- 4 r- m co o o CM o CO in o in o co ro eg c\j in in co ro sU CO cr co CO in vO CO CO o o o o o o o o c o o o o o o o o o o o o o o o ,-4 r- r- co m o cm o ^ co o ^ cr* r— co co cr in c\i co co co Is- o •£> o o Is- cr- cnj o m co ro vO NO cm ro in co ro sD O in cm in co o o o o o CT ro in cm in O cm m o 00 O CM ro i— 1 O in >t O CM CM CO CM CM CO CO CO ro to O vO <4- ro -4- O o o o in i~t r\j CM c<~ ro •-4 r- CO r- CO CO v.0 vO in in in h- vD sO vO vO cr cr- Is- o ro o CO o in o h- r- Is- Is- Is- O CO CO h- CO sO r1- a> r-l ro sf ro Is- CO >t o cr- ro in in »t in in 4 in ■sT ro 0' a m m o in vO r-4 r- CM r-4 CM CO O r—l CO ^-1 f-( r-f IM CM CM 83 00 CM p~ CM CO vC O CO cr P- st st in CO Cr in CO st ITi in CO Z M • • • t « • ro m CM (Ml CM CM CM CM st CM ro CO CM rO r\j CO ro ro CM rH CO p~ p- CO st st rH v0 CO vO co rH CM O r- r- r-4 CO o co in rH vO rH i— t CM r-< t—i CM l-l r-i i— i v0 o in st m in vO r- o in in in in O vO O 0 o rH cr ro o st cr CO v0 r-i r- 00 cr st ^0 CM CM rH ro CM r-l CM CM i-< CM st CO CM CO ro ro st ro ro in st CM 0 CO CO h- CO CO r- P- CO P- /»V st O CO o CO -4- CM CT> o o o o O o o o O o o O O vO s0 p~ vO CO o CM in in o CO in o 0- CO m r- ro o rH 'cr PL. C\l CM CM CM CM C\J CO CM in sO in st in st in IT, in st in in st •~\ (NJ ro o CM ITi vO 0^ (M o o O o o o O o o o o o o s-s V— / CM p- in ro st si- CO ro CO vt in 0> r~ CO rH in o CO rH P- o ►J ►J st cr in CM st in o tn o- xO vO ro CO cr O in o CO in vw vC vO in st in in st st eH CM ro st CO st rH ro in in in st CO CO X p~ r— I vO .h v0 r-l in o CO O ro ir> aj o co o ro in CO o CM *J *-s O. G o r- p- co CO CJ- cr o C^ cr st Cr st a ro Cr st cr st o in OJ o cm LO CO i— « st p- O •4- rH ro st s0 CO H co st o CO cr Q sw rH rH rH CM CM i • U-l \o rs. CO a; o lO m m a; ss 84 CO rH O o ■—( r-l in T~4 O r^, CM o C\J in O in w r\J i— i r^ •4- 4" CO m o in CM m CM in >d- s* CO IT. ro -4- ro in M" sf CM vT in CM M rH rH rH r— 1 rH i—i r— t r— i r-l r-l rH rH rH rH rH rH O r- v0 in r- 00 vO in O CM 1*- O ro m r- O vf in >t o ■4- O CO ■tf r-< sO 5 o o in •4- o T st ro o- -4- ■4- ro CO en ^" -4- t r-l T-4 rH i— i rH rH r-l T—l rH rH H rH /""> vO rH cc CO •4" CO o vO nO CO vO «fr ro CO en >>-' O CM ^o CM O CM o Is- 0* cr in CM m vO CO r~i m 52 cn CM (M CO CM CM CM CM CM m CM rH CM rH CM CO CD CM CM O r-i ITi CM CM CM r— 1 «o en vO •4- O CM sO co •4" vj- m CM •4- 4" Is- CM >t en c o CM CT' Is- (NJ CM CM l-< en w* CM rH CM CM CM CM en CM rH <-* B o o O o o o o o O O O O o O O o g o o O o o o o o O o o c o C O o • • * • • • • • • « • • c c • • o o o o a o o c o o o o o O o c CO o § en Is- o vt Q> 0s 1—1 r-l m rH Is- Is- cr en 0^ o CM 00 O CO CD CO CO cc CO 0' o S-5 CM f-t in rH o c in 0^ •t i— 1 CM in CO Is- en CM >«• • Is- CO i— t CM v0 i-H CO o CM rH O 0s Is- Is- o en ►J P-. m st Sf ^r en •st- en •4- «t ^ n0 en Is- CM rH en co B^S ■ ■ • « • • • • • N^ »—i CO o t> v0 O en en Is- sf! 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W. , "Engineering Geology of San Francisco Bay Calif o,. .ia," Bulletin of the Geological Society of Amc-rica, v. 162, p. 1079-1109," 1951. Tschebotariof f , G. P., Soil Mechanics, Found at J .n-~s ar. ' Earth Stru^.' -'res, McGraw Hill, New York, p. 226, 1951. ~ Wins low, J. D. and Gates, G. R. , "Effect of Soil rehydration on Atterberg Limits," Materials Research and Standards, v. 3, No. 3, p. 205-210, March 1963. 101 INITIAL DISTRIBUTION LIST No. Copies 1. Defense Documentation Center 2 Cair,( ron Station Alexandria, Virginia 22314 2. Library, Code 0212 2 Naval Postgraduate School Monterey, California 93940 3. Oceanographer of the Navy 1 The Madison Building 732 North Washington Street Alexandria, Virginia 22314 4. Professor R. J. Smith (Code 58Sj) 3 Department of Oceanography Naval Postgraduate School Monterey, California 93940 5. LCDR Robert W. Iloag II, USN 8 % 35 E. Pierson St. Phoenix, Arizona 85012 6. ProfesE-r R. S. Andrews (Code 58Ad) 3 Do nt of Oceanography Nav,-i i Postgraduate School Monterey, California 93940 7. Commander 10 Naval Facilities Engineering Command Code 03 Washington, D. C. 20390 8. Departmc :l: of Oceanography (Code 58) 3 Naval Postgraduate School Monterey, California 93940 102 UNCLASSIFIED Security Clai sifi< DOCUMENT CONTROL DATA -R&D M-i hum- classification ot title, '■ rfj f abstract itnil indexing annotntion must he entered when the overt' II r -port Is classified) I originating activity ( Corpora te author) Naval Postgraduate School Monterey, California 93940 :::. I I PONT SECURU 1 ( I UNIFICATION Unci assif led 2b GROUP 3 REPORT TITLE Estimation of the Original Shear Strength of D< sp Sea Sediments from Engineering Index Proper ties * DESCRIPTIVE NOT! >| . ' of report and, incliis i \ ■ dales) Master's Thesis; September 1970 5 AUTHC^ISI fFifsfnsmf, middle initial, last noire) Robert Wyman Koag II 6 REPOR T DATE September 1970 ?«. TOTAL NO. OF PAGES 103 7b. NO. OK REFS 54 8a. CONTRACT OR GRANT NO. 6. PROJEC T NO 9a. ORIGINATOR'S REPORT NUMDL'.R(S) 9b. OTHER REPOi. • i I (Any other numbers that may be assigned th:.~ report) 10 DIS1RIBUTION STATEMENT This docu ent has been approved for public release and sale; its distribution is unlimited II. SUPPLEMENTARY NOTES 12. SPONSORING MILI'; v ACTIVITY Naval Postgrad ite School Monterey, Cali ornia 93940 13. A B S . :"< A C T Multiple linear regression techniques were employed in a statistical analysis of data from 114 deep sea cores in order to derive an equation for predicting shear strength from sediment engineering index properties. Water content, depth of burial, liquid limit, and plastic limit proved to be the only factors significantly influencing the streng. h in these core?. The multiple and individual correlation coefficients between these four parameters and the logarithm of shear relation. Additionally, other regression analysis were conducted to determine a wrier content prediction equation and to investigate correlations among other sediment properties. Water content is shown to be highly correlated with liquid limit. Ancillary to the above analysis, tests where conducted to determine the degree of reproducibility of original liquid limit values from dried sediment material . DD ,?„?..1473 S/N 01 01 -C07-G81 I (PAGE 1) 103 UNCI/' SSIFIED Security Classification 1-81(0' UNCLASSIFIED Security Clsssificetion key wo RDS Atterberg limits Cores Data Deep sea cores Deep sea sediments Engineering properties of marine sediments Liquid limit Marine sediments Regression analysis Reproducibility of sediment properties Sediment engineering proper Lies Sediment cor Sediments Shear strength Shear strength prediction Statist' 1 analysis Water content Water content prediction L I IV K A LINK B LINK C \J &■/ t NOV 68 S/N 01 0 1 - R0 7- £, «;> | 1473 (DACK 104 UNC> IED Security Classification A- 3 I 409 s Thesis H585 ^•2L''0- Hoag Estimation of the o- riginal shear strength of deep sea sediments from engineering index properties. 3 DEC 71 < 4UCT 72 4 ' < T 72 2 1 8 U 0 2 1 8 U 0 n o ? 't o Thesis H585 Hoag Estimation of the o- riginal shear strength of deep sea sediments from engineering index properties. ■ 0 thesH585 Estimation of the oriental shear strengt 3 2768 002 06803 3 DUDLEY KNOX LIBRARY