Geo-Congress [978-0-7844-1329-6.001]

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Characteristics and Intercorrelations of Index Properties for Cohesionless Gravelly Soils

Jie-Ru Chen1, A.M.ASCE and Fred H. Kulhawy2, Dist.M.ASCE, P.E., G.E.

1Associate Professor, Department of Civil Engineering, National Chi Nan University, 1 University Road, Puli, Nantou, Taiwan 54561, R.O.C.; email: [email protected] 2Professor Emeritus, School of Civil and Environmental Engineering, Hollister Hall, Cornell University, Ithaca, New York 14853-3501; email:[email protected] ABSTRACT: Several index properties for gravelly soils, and factors affecting them, are examined, including the unit weight (γ), void ratio (eo, emax, emin), and porosity (no). A database of 43 sandy and gravelly soils from 36 sites with 137 individual soil samples was employed, along with additional laboratory data, for this examination. It was found that these indices are largely a function of the soil gradation properties, geology, and age. Correlations among these indices and several gradation properties (D50, Cu, angularity) also can be established. Unfortunately, particle shape data are limited, so the influence of this parameter can only be understood qualitatively. However, the developed correlations are useful for estimating the index properties for a wide range of cohesionless sandy and gravelly soils. INTRODUCTION The behavior of soils is influenced by basic soil index properties and the environmental conditions, such as depositional and diagenetic processes. These indices allow for basic site characterization and for interpreting soil performance properties such as strength and stress state. For cohesionless soils, key indices are the dry unit weight (γd), in-situ porosity (no), and limiting densities (emax, emin, and emax - emin). Moreover, gradation properties, such as particle size, shape, and composition, are important influences on soil behavior. However, testing for these indices is not common when gravelly soils are encountered. To enhance our understanding of these index properties for gravelly soils, a large database was compiled to examine these issues. In this paper, the factors influencing the index properties were explored using the database. Useful correlations were developed and are discussed herein. These are basically a function of the soil gradation properties, geology, and age. DATABASE To examine the index properties of granular soils, a literature search was conducted to develop a database of quality information for natural soils. This search resulted in a database of 43 sandy to gravelly soils from 36 sites, which included individual

1Geo-Congress 2014 Technical Papers, GSP 234 © ASCE 2014

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measurements of index properties for more than 137 soil samples. Data regarding the soil, site, sampling, in-situ testing, and geology were summarized for each sample. Details are too lengthy to list herein, but they are given elsewhere (Chen 2004). For convenience, the range of essential information is summarized in Table 1. These soils originate from the U. S., Canada, Japan, and U. K., and they were deposited under various geological environments (including man-made, fluvial, aeolian, glacial, and volcanic processes) over a wide range of geological time (from less than a year up to the Jurassic period). After preliminary analysis, these soils were sub-divided into four types based on the nature and origin of the deposit. The first two are “fill” and “tailings”, which are “created” soil deposits. The fills are mainly reclaimed landfills formed using various hydraulic filling techniques, which may or may not be compacted subsequently. The tailings are hydraulically placed sand deposits from the mining industry. The third is “native” soil of fluvial, aeolian, or glacial origin; fluvial dominates in this database. And fourth consists of native “volcanic” soils, which warrant a separate population. To illustrate the range of these soils, the coefficient of uniformity (Cu) for each was plotted vs. its corresponding mean particle size (D50) in Fig. 1. Grouping was done based on the deposit type and age, as noted by the symbols, and sandy soils are separated from the gravelly soils. The result is eight major groups for this study: (a) geologically aged sand (older than Quaternary), (b) Quaternary sand, (c) Quaternary gravel, (d) sand fill, (e) gravel fill, (f) tailing sand, (g) volcanic sand, and (h) volcanic gravel. Granular soils were considered well-graded with Cu > 6 for sandy soils and > 4 for gravelly soils. A horizontal dashed line at Cu = 4 in Fig. 1 separates the poorly-graded (uniform) soils below from the more well-graded soils above. Two vertical dashed lines at D50 = 0.3 and 1.0 mm also are plotted; these will be discussed later. As shown, Cu generally increases with D50. Note that there are two blank regions with no data. Region I represents fine sand with significant fines. Silt and clay are

Table 1. Summary Information of Data Range for Compiled Soil Data

Item Gs D50 (mm) Cu eo no (%) emax emin γd (kN/m3) Dr (%)

Sand (total samples = 66) n 64 66 65 64 64 39 39 64 66

Mean 2.64 0.31 3.48 0.990 48.7 1.175 0.701 13.2 65 S.D. 0.10 0.13 3.30 0.314 6.9 0.346 0.222 2.2 19 Max 2.77 0.70 18.00 1.988 66.5 2.389 1.451 17.3 115 Min 2.40 0.15 1.20 0.521 34.3 0.836 0.461 8.1 26

Gravel (total samples = 71) n 68 70 68 68 68 41 41 70 71

Mean 2.66 7.52 45.26 0.374 27.1 0.573 0.339 19.1 71 S.D. 0.04 5.87 71.92 0.063 3.4 0.116 0.092 1.0 26 Max 2.86 25.00 380.00 0.519 34.2 0.859 0.535 21.4 121 Min 2.62 0.32 1.90 0.212 17.5 0.403 0.194 17.1 10


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FIG. 1. Grain size characteristics of soils compiled for this study.

likely soils within this region; measurement of their relative density is not advised. Region II represents very uniform gravelly soils, which may not exist in natural field conditions. Note that the Quaternary sands are mainly uniformly graded, while the Quaternary gravels tend to be well-graded. EVALUATION OF DRY UNIT WEIGHT (γd)

The soil dry unit weights (γd) were plotted vs. grain size properties in Fig. 2, with D50 in Fig. 2a and Cu in Fig. 2b. The differences in γd are clear through the groupings. In general, γd increases with an increase of D50 or Cu. Excluding the aged sands and the volcanic sands and gravels, the remaining soils can be considered together, as they all are Quaternary deposits that are relatively young geologically and would be expected to have experienced only a modest amount of stress history alteration. As noted previously, the Quaternary sands are mainly uniformly graded, while the gravels are well-graded. In Fig. 2a, two vertical lines separate these Quaternary soils into three regions. When D50 is less than 0.3 mm, they are mainly uniform sands. When D50 is greater than 1 mm, they are mainly well-graded gravels. The trend of increasing γd with D50 is clear for these two soils. However, when D50 is between 0.3 and 1 mm, the two types of soils present, uniformly-graded coarse sands and gap-graded gravelly sands, showed very different unit weights. To examine further the differences of γd for these two types of soils, consider Fig. 3, which shows the grain size distributions and ranges of variation of three major types of cohesionless soils considered herein. As shown, very comparable D50 and Cu exist for both the gap-graded gravelly sands and the uniform sands, since the grain size curves overlap at less than about D60 to D50. However, the coarser fraction for the gravelly sand covers a wider range of grain size, resulting in different γd. The dry unit weight of Quaternary sands typically ranges from 13 to 16 kN/m3, while that of Quaternary gravels ranges from 18 to 22 kN/m3. Regression analyses


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(a) γd vs. D50 (b) γd vs. Cu

FIG. 2. Dry unit weight vs. grain size properties for cohesionless soils. were conducted using all of the Quaternary data to evaluate the relationship between γd and D50. The following logarithmic equation depicts the general trend of the data:

γd = 16.5 + 3 log(D50) r2 = 0.729 (1)

in which the units of γd are kN/m3 and the units of D50 are mm. As shown in Fig. 2a, the regression fits well throughout the uniform sands and well-graded gravels. For soils with D50 between 0.3 and 1 mm, values estimated from Eq. 1 overestimate γd for uniform soils and underestimate γd for well-graded soils. To use the regression for soils with D50 between 0.3 and 1 mm, subtract 1 kN/m3 from γd to correct the overestimation for the uniform soils and add 2 kN/m3 to correct the underestimation for the well-graded soils. These modifications can provide a first-order estimate of γd for Quaternary cohesionless soils. Fig. 2a also shows that two soil groups, aged sands and volcanic sands, differ from the Quaternary soils. The aged sands have a nearly parallel variation with D50 as the Quaternary sands. However, they are much older and have experienced more stress history-induced alteration, resulting in lower porosity and increased γd. As shown in Fig. 2a, γd for these soils is about 3 kN/m3 greater than the average γd of Quaternary sands. The volcanic sands have a much lower γd that is largely because of their high depositional void ratios. There is no clear correlation between γd and either D50 or Cu, although γd is on the order of 10 kN/m3. For general comparison, the typical ranges of γd suggested by Hough (1969) are shown by the horizontal lines in Fig. 2b. These lines bound the data well, except for the volcanic sands.


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FIG. 3. Range of grain size distribution for three main types of soils.

ANALYSIS OF ADDITIONAL UNIT WEIGHT DATA Additional data for gravelly soils were used in this study. These soils were not included in the main database, because there is insufficient exploration data for these cases, especially for the limit density data. These additional soils are mainly gravels and cobbles with a maximum particle size range of 50 to 500 mm, which extends the data to a greater size range. Moreover, these data are from locales where gravelly soils are of major engineering concern, including: (a) Messina Straits in Sicily, (b) metropolitan Santiago, Chile, (c) western Taiwan, and (d) various projects along gravel-deposited rivers in India and Pakistan. A total of 34 additional soils are included, with detailed information in Chen (2004). Because of the large particle size, the unit weights were measured in-situ using various types of replacement methods (e.g., sand or water). Moreover, it is commonly found that these soils are gap-graded with missing middle-sized ranges, from fine gravel (3 mm) to medium sand (0.25 mm). The measured dry unit weights for these additional coarse soils, grouped into quartzitic and lateritic gravels, were plotted vs. D50 and Cu in Figs. 4a and b, with all the soils plotted in Fig. 2. These additional data extend the plot into the large particle size range, but the scatter is somewhat greater. To discuss these data further, additional factors need to be considered, such as the depositional histories and mineralogical details. The Messina Straits gravels are coastal plain deposits (Crova et al. 1993). The soils near Santiago, Chile and near rivers in Pakistan and India are fluvial (Rodriguez-Roa 2000, Agha & Masood 1997, Mohan et al. 1971). The remaining soils are surficial deposits from the northern to middle-south of the western foothills or basins of Taiwan. These gravelly soils are associated with coastal or river terraces and alluvial plains. Geologic details are given in Ho (1975). The terrace deposits are Pleistocene and have been differentiated into lateritic and non-lateritic. The non-lateritic terrace deposits are composed largely of unconsolidated gravel with flat-lying sandy or silty lenses, and they generally are not stratified. In the lateritic terrace deposits, red matrix clay is developed in the


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(a) γd vs. D50 (b) γd vs. Cu FIG. 4. Dry unit weight vs. grain size properties for cohesionless soils, with

extended database. surficial part of the gravel. In a complete profile, the laterite grades downward into red matrix clay, filling the gravel voids, and further downward to the unweathered gravel. The other forms of gravelly soils that cover the coastal plains are the alluvial deposits, described as alluvium by Ho (1975). The alluvium forms the flood plains and recent terraces of many leading streams all over Taiwan (Ho 1975), and its geological age is relatively younger Holocene.

All of the gravelly soils from Taiwan have similar grain size characteristics, but they are still categorized into three groups. The first group is lateritic gravelly soils, which were found largely in terraces in northwest and middle west Taiwan. These soils normally contain plastic fines and are denoted “lateritic terrace”. The second group represents the “alluvial fan” deposits, which are largely found in the city of Taichung. These deposits are normally non-plastic. The third group is somewhat on the borderline. These are called “quartzitic gravel” instead of “lateritic gravel”. The lateritic gravels were plotted using different symbols (open circles) in Fig. 4. As can be seen, γd of lateritic gravels is consistently lower than that of non-lateritic gravels, which matched well the relationships for the Quaternary sand and gravel. This difference can only be identified when the soil geology is considered. The in-situ γd also can be interpreted by considering the mean value for a particular type of soil. The descriptive statistics for γd of all soils herein are summarized in Table 2. As can be seen, the standard deviation for each group is fairly small when the groupings consider both the grain size and geology. This table provides a simple first-order estimate of the dry unit weight for these coarser cohesionless soils.

EVALUATION OF IN-SITU POROSITY (no) The measured no values were plotted versus the estimated geologic age in Fig.5 for all samples summarized in Table 1. These age data were compiled for this study, with details in Chen (2004). Some ages were estimated through common dating


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Table 2. In-Situ Dry Unit Weight for Various Types of Cohesionless Soils

Material n γd (kN/m3) S. D. COV

max min mean (%) Quat. uniform sand (fine to coarse) 31 15.5 12.4 14.0 0.9 6.3 Pre-Quaternary fine sand 6 17.3 16.7 17.0 0.2 1.4 Gap-graded gravelly sand 6 18.5 17.1 17.8 0.6 3.1 Quaternary sandy gravel 56 21.4 17.7 19.1 0.9 4.5 Gravelly cobbles 26 22.7 17.8 20.8 1.2 6.0 Lateritic gravel and cobble 8 21.2 17.3 18.2 1.3 6.9 Volcanic sand 15 13.4 8.1 10.3 1.6 15.4

FIG. 5. In-situ porosities vs. age for sands and gravels.

techniques, while others were estimated from their stated geologic age. Note that for the aged sands from the U. K. (Barton & Palmer 1989, 1990, Palmer & Barton 1987), the in-situ porosities are much lower than those for the Quaternary sands. The native sands and the created (fill and tailings) deposits cover the full Quaternary period, and they have very similar in-situ porosities. Two horizontal lines are shown in Fig. 5 that delineate the original depositional porosities for sands of various origins, which generally are in the range of 40 to 50% (Friedman & Sanders 1978, Pryor 1973, North, 1985). As shown, the measured no for these native and created Quaternary sands fall within this general range. The no of the volcanic sand is consistently higher than native soils of the same age, because of the highly porous structure that is formed during deposition. The no for the gravelly soils, which range between 20 and 35% are consistently lower than those for the Quaternary sands. A useful aspect of the porosity is to compare the value measured in-situ with the original depositional state. The difference between these two values would suggest the diagenetic influences for the given soil deposit. However, much more research is needed to quantify this effect. Fig. 6 shows the influence of D50 and Cu on no for all of the coarser cohesionless


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soils. The ranges of the original depositional porosity for sands are also shown as dashed lines. As shown, the effect of the grain size properties on the in-situ porosity is similar to that on the dry unit weight, with porosity decreasing in general with increasing particle size and uniformity. Distinct groupings also are prominent. MEASUREMENT AND EVALUATION OF LIMITING DENSITIES The soil data were collected from various sources, and therefore the limiting soil densities were measured by several different approaches. For sands, these included the approaches developed by Ishihara et al. (1978), proposed by Kolbuszewski (1948), and suggested by major standards (ASTM, Japanese, and British). For gravelly soils, various approaches modified the standard tests for sands and used enlarged apparatus. Although it is well-recognized that there are differences in the limiting densities measured using different approaches, no general procedure is available for correcting these differences. However, since the measured densities come in pairs, it is reasonable to examine the consistency in obtaining the pair of test results for each soil. The maximum dry unit weights were plotted vs. the minimum dry unit weights in Fig. 7 for natural soils (denoted “Field Data”) summarized in Table 1. As can be seen, the two limiting properties are strongly correlated and can be described by linear interrelationships. Similar interrelationships have been presented by other authors. However, the previous results were obtained either from testing on the same sand (Poulos & Hed, 1973) or from testing over a wide range of sand in the laboratory (Maeda 1994, Miura et al. 1997). Although their data were limited, Poulos & Hed (1973) suspected that a unique interrelationship could be obtained for a wide range of cohesionless soils. It is somewhat surprising to see a linear correlation between the limiting densities for such a wide range of cohesionless soils, especially when tested using several somewhat different approaches. Based on the consistency of these results, it appears that the limiting densities for these soils can be examined together, regardless of test variability. Linear regression analyses were conducted using all of the data, and the results are shown in Fig. 7. Regressions using two types of linear

(a) no vs. D50 (b) no vs. Cu

FIG. 6. In-situ porosity vs. grain size properties for cohesionless soils.


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FIG. 7. Maximum vs. minimum dry unit weights for cohesionless soils.

equations (best fit and through origin) were performed on each set of data. The linear equation through the origin described the correlations slightly better. This type of correlation has been suggested previously (e.g., Maeda 1994, Miura et al. 1997). To examine this interrelationship further, additional available laboratory data from the literature (denoted “Lab Data”) were compiled and plotted together with the field data in Fig. 7. Even with some scatter, the regression equation through the origin still seems to describe the correlation fairly well. Fig. 8 shows the maximum and minimum void ratios vs. Cu. The values for volcanic sands were higher than all other types of soils, as discussed previously. It is interesting to note that the different characteristics for these soils followed through to the measured limiting void ratios, which were determined under fully reconstituted conditions. Therefore, it is not surprising that the computed values of relative density for these volcanic sands fall within the normal range (0 to 100 %). The trend of all

(a) emax vs. Cu (b) emin vs. Cu

FIG. 8. Limiting void ratios vs. coefficient of uniformity for cohesionless soils.


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the other field data is the same as that observed in prior studies, which show both the maximum and minimum void ratios decreasing with increasing Cu. There is no age effect on the maximum and minimum void ratios, because any structure existing in-situ is destroyed when the soils are reconstituted in the laboratory. The curves for estimating maximum and minimum void ratios proposed by Youd (1973) also were plotted in Fig. 8. In each plot, two curves were shown, with one corresponding to the relationship for angular particles (R = 0.17) and the other for well-rounded particles (R = 0.7). For these limiting particle shapes, the data were bounded within the curves. Unfortunately, because of the lack of data on particle shape, the effect of soil angularity can not be explored any further. In addition, regression analyses were conducted on the data in Fig. 8, and the results are shown in the figures. Although there is some scatter, Cu has been identified as the main influencing factor by many authors. The established correlations should only be used as a first-order estimation. The influence of particle size on the maximum and minimum void ratios were found to be similar to those between the limiting void ratios and Cu. This similarity can be expected because Cu is positively correlated with D50 for the compiled data, as shown in Fig. 1. In general, the limiting void ratios decrease with increasing D50 for the native and created soil deposits. The void ratio range was suggested to be a primary soil index property by several authors (Yoshimura & Ogawa 1994, Maeda 1994, Cubrinovski & Ishihara 1999) and was used to establish interrelationships with other soil properties. Void ratio range is defined as the difference between the maximum and minimum void ratios (emax - emin), which represents the compressibility of a soil. The void ratio range is plotted vs. the grain size properties in Fig. 9. These plots show similar characteristics as those for emax and emin, and the void ratio range decreases both with increasing Cu and D50. Attempts have been made to establish the correlations between the void ratio range and grain size properties. Regression analyses were done for the void ratio range and both Cu and D50 using all of the data, except for the volcanic soils. The resulting curves are plotted in Fig. 9 and are given below:

emax - emin = 0.24 + 0.34 / Cu, r2 = 0.560 (2) emax - emin = 0.25 + 0.038 / D50 r2 = 0.578 (3)

In Fig. 9b, a curve also is shown that describes the relationship between the void ratio range and D50 proposed by Cubrinovski & Ishihara (1999). In general, these correlation equations capture the main trend between the parameters, but there is variability. Since there is a linear relationship between emax and emin as discussed previously, the void ratio range is expected to be influenced by all the factors influencing the maximum and minimum void ratios. Factors such as grain shape may need to be considered to further develop these correlations.


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(a) (emax - emin) vs. Cu (b) (emax - emin) vs. D50

FIG. 9. Void ratio range vs. grain size parameters for cohesionless soils. NEEDED STUDIES TO IMPROVE PROPERTY EVALUATION To understand the index properties of gravelly soils better, several areas need to be researched further. First are the maximum and minimum densities that need to be measured for estimating the relative density of cohesionless soils. Standard procedures for measurement are available for sandy soils, such as ASTM D4253 and D4254. High quality gravelly soil samples have been obtained using newer freezing techniques, but density measurement basically is the same. Improved procedures are needed. The limiting densities are influenced by basic soil particle characteristics. The coefficient of uniformity and particle shape appear to be the two main factors controlling these limiting densities. There were already significant data to delineate the influence of coefficient of uniformity; however, the influence of particle shape was only understood to a qualitative level. This and other studies (Maeda 1994, Cubrinvoski & Ishihara 1999) have shown that the influence of particle shape needs to be explored to establish more accurate interrelationships between the limiting densities and basic soil properties. Detailed studies on particle shape are needed.

SUMMARY AND CONCLUSIONS The index properties for cohesionless soils ranging from sands to gravels were examined. A database was compiled that consisted of 43 sand and gravelly soils from 36 sites with 137 individual soil samples. This database, along with additional laboratory data, was used for detailed examinations of the index properties. Parameters examined include the dry unit weight (γd), in-situ porosity (no), and the limiting densities. These index properties basically are a function of grain size properties, and it was found that various parameters (D50, Cu, angularity) are useful to establish relationships with these index properties, along with soil geology and age. For Quaternary cohesionless soils, a correlation exists between γd and D50. In general, γd increases with increasing D50, and their interrelationship can be established by a


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logarithmic equation. A table also was developed that can be used to estimate γd based on the type and age of the cohesionless soils. The in-situ porosity was found to be a function of the particle size and age of the soil deposit. A useful aspect of the porosity is to compare the value measured in-situ with the original depositional state. The difference between these two values would indicate the diagenetic influences for the given soil deposit. However, more research is needed to quantify this effect. Limiting densities are significant properties for the determination of the relative density of cohesionless soils. It was found that there is a linear relationship between the limiting densities. It also was found that the limiting void ratios are controlled by the uniformity coefficient and particle shape. Unfortunately, existing data are not sufficient to assess particle shape, so this factor can not be quantified further at this time. REFERENCES Agha, A. & Masood, T. (1997). “Estimating engineering characteristics of gravelly

soils”, Proc., 14th Intl. Conf. Soil Mech. Geotech. Eng., 1, Hamburg: 9-12. Barton, M.E. & Palmer, S.N. (1989). “Relative density of geologically aged, British

fine & fine-medium sands”, Quart. J. Eng. Geol., 22(1): 49-58. Barton, M.E. & Palmer, S.N. (1990). “Geotechnical investigation of geologically

aged, uncemented sands by block sampling”, Proc., 6th Congress Intl. Assoc. Eng. Geol., 6, Amsterdam: 281-288.

Chen, J.R. (2004). “Axial behavior of drilled shafts in gravelly soils”, Ph.D. Dissertation, Cornell University, Ithaca, NY.

Crova, R., Jamiolkowski, M., Lancellotta, R. & Lo Presti, D.C.F. (1993). “Geotechni-cal characterization of gravelly soils at Messina site”, Predictive Soil Mechanics, Thomas Telford, London: 199-218.

Cubrinovski, M. & Ishihara, K. (1999). “Empirical correlation between SPT N-value & relative density for sandy soils”, Soils & Fndns., 39(5): 61-71.

Friedman, R.W. & Sanders, J.E. (1978). Principles of Sedimentology, Wiley, New York: 792 p.

Ho, C.S. (1975). Introduction to Geology of Taiwan – Explanatory Text of Geologic Map of Taiwan, Ministry of Economic Affairs, ROC, Taipei: 153 p.

Hough, B. K. (1969). Basic Soil Engineering, 2nd Ed., Ronald Press, NY: 634 p. Ishihara, K., Silver, M.L. & Kitagawa, H. (1978). “Cyclic strengths of undisturbed

sands obtained by large diameter sampling”, Soils & Fndns., 18(4): 61-76. Kolbuszewski, J. (1948). “Experimental study on maximum & minimum porosities of

sands”, Proc., 2nd Intl. Conf. Soil Mech. Fndn. Eng., 1, Rotterdam: 158-165. Maeda, K. (1994). “A study on deformation-failure behavior of sands with different

primary properties”, Doctoral Thesis, Hokkaido University, Sapporo, Japan. Miura, K., Maeda, K., Furukawa, M. & Toki, S. (1997). “Physical characteristics of

sands with different primary properties”, Soils & Fndns., 37(3): 53-64. Mohan, D., Narahari, D.R. & Rao, B.G. (1971). “Field & laboratory tests on gravel &

boulder soils”, Proc., 4th Asian Conf. Soil Mech. Fndn. Eng., 1, Bangkok: 49-55. North, F.K. (1985). Petroleum Geology, Allen & Unwin, Boston: 607 p. Palmer, S.N. & Barton, M.E. (1987). “Porosity reduction, microfabric & resultant


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lithification in UK uncemented sands”, Diagenesis of Sedimentary Sequences, Spec. Pub. 36, Geol. Soc., London: 29-40.

Poulos, S.J. & Hed, A. (1973). “Density measurements in a hydraulic fill”, Relative Density & Its Role in Geotechnical Projects Involving Cohesionless Soils (STP 523), ASTM, Philadelphia: 402-424.

Pryor, W.A. (1973). “Permeability-porosity patterns & variations in some Holocene sand bodies”, Bull. Amer. Assn. Petroleum Geol., 57(1): 162-189.

Rodriguez-Roa, F. (2000). “Observed & calculated load-settlement relationship in a sandy gravel”, Can. Geotech. J., 37(2): 333-342.

Yoshimura, Y. & Ogawa, S. (1994). “Influence of primary properties on void ratio & shear characteristics of granular materials”, Japanese J. Civil Eng., 487(III-26): 99-108. (In Japanese)

Youd, T.L. (1973). “Factors controlling maximum & minimum densities of sands”, Relative Density & Its Role in Geotechnical Projects Involving Cohesionless Soils (STP 523), ASTM, Philadelphia: 98-112.


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Geo-Congress [978-0-7844-1329-6.001]