maximum and minimum void ratios and median grain size of

3rd International Conference on New Developments in Soil Mechanics and Geotechnical Engineering,

28-30 June 2012, Near East University, Nicosia, North Cyprus

37

KEYWORDS: Maximum void ratio, minimum void ratio, median grain size, idealized spheres,

angularity, volumetric strain potential, compaction, cone penetration test

ABSTRACT: The relationships between maximum and minimum void ratios of granular soil with various percentages of fine contents have been presented. The maximum and minimum void ratios are functions of soil properties such as grain size distribution, uniformity coefficient, angularity, and percentage of fine contents. Based on the existing results, it appears that the difference between the maximum and minimum void ratios, not maximum void ratio or minimum void ratio alone, is the controlling parameter for compressibility, relative density, and strength of granular soils. In spite of some scatter, the difference between the maximum and minimum void ratio bears a unique relationship to the median grain size. Several correlations relating the median grain size with the strength and compressibility are presented.

1 INTRODUCTION

According to the Classification System of Soils and Soil-Aggregate Mixtures for Highway Construction Purposes provided in Test Designation D-3282 [(ASTM 2010); also referred to as AASHTO Classification System], sand is defined as particles passing 2-mm sieve (US No. 10) and retained on 0.075-mm sieve (US No. 200). Particles that pass through 2-mm sieve (US No. 10) and are retained on 0.425-mm sieve (US No. 40) are defined as coarse sand. Similarly, particles passing 0.425-mm sieve and retained on 0.075-mm sieve are fine sand. However, according to the Unified Soil Classification System (ASTM D-2487), sand particles can be divided into the following three major categories:

Coarse sand: Particles passing through 4.75-mm sieve (US No. 4) and retained on 2-mm sieve (US No. 10);

Medium sand: Particles passing through 2-mm sieve (US No. 10) and retained on 0.425-mm sieve (US No. 40); and

Fine sand: Particles passing through 0.425-mm sieve (US No. 40) and retained on 0.075-mm

sieve (US No. 200). From the viewpoint of soil-separate size limits, the US No. 10 sieve (2-mm opening) is the more-accepted upper limit for sand. In nature, sand is generally a combination of particles of variation sizes and shapes and may contain some plastic and/or non-plastic fines. The stress-strain behavior of sand is primarily a function of the following: grain-size distribution, fine content, shape of grain angularity, mineralogy, relative density (Dr), and state of effective stress.

Maximum and minimum void ratios and median grain size of granular soils: their importance and correlations with material properties

B.M. Das California State University, Sacramento, USA,[email protected]

N. Sivakugan

James Cook University, Australia, [email protected]

C. Atalar

Near East University, North Cyprus, [email protected]



38

In many cases the behavior of sand is represented by one or two parameters such as fine content (Fc) and the uniformity coefficient (Cu) without consideration to other material properties. It has been clearly pointed out by Cubrinovski and Ishihara (1999, 2002) that two sand samples with identical fine contents (Fc) can show remarkably different stress-strain characteristics. For that reason they suggested that emax – emin (emax = maximum void ratio and emin = minimum void ratio) and, hence, the relative density may be a more appropriate parameter to describe the behavior of sand. In addition, relative density indicates the relative position of field void ratio between emax and emin and is defined as

minmax

max

ee

eeD

r

(1)

where e = in situ void ratio The minimum and maximum void ratios can be determined respectively according to the procedures given by ASTM test designations D-4253 and D-4254. These test methods are applicable to soils that may contain up to 15%, by dry mass, of soil particles passing 0.075-mm sieve (fines). However, there are other methods in use to obtain emax and emin. The Japanese Geotechnical Society (2000) has a test method to obtain emax and emin with less than 5% fines. These methods may provide slightly different values for the extreme void ratios. The purpose of this paper is to review the general nature of variation of emax, emin, and emax – emin of sand and the factors controlling them. The importance of emax, emin and the median grain size (D50) of several material properties will be discussed.

2 MAXIMUM AND MINIMUM VOID RATIOS OF IDEALIZED SPHERES

In order to understand the factors on which the values of emax, emin, and emax – emin of soil particles depend, it is desirable to initially evaluate the void ratio variation of idealized spheres. Graton and Fraser (1935), White and Walton (1937), and McGeary (1961) have studied this in detail. It has been recently well summarized by Lade et al. (1998). Figure 1 shows the five possible modes of packing of single-sized spherical particles along with the void ratio for each type of packing. They are

1. Simple cubic (e = 0.91)—This is the loosest possible form of packing. 2. Single stagger (e = 0.65)—In this packing, each sphere in its own layer touches six other

spheres. The spheres in consecutive layers are stacked directly over each other. 3. Double stagger (e = 0.43)—It is similar to single stagger. However, each sphere in a layer

slides over and down to contact two spheres in the second layer. 4. Pyramidal (e = 0.35)—In this packing, each sphere in a layer lies over the depression between

and is in contact with four spheres in the layer below. 5. Tetrahedral (e = 0.35)—This is similar to pyramidal packing. However, each sphere in one

layer lies in the depression between and is in contact with three spheres.

.

Figure 1. Possible modes of packing of single-size spherical particles (adapted from Lade et al. 1998).

McGeary (1961) performed tests of single-sized spheres to determine its minimum void ratio [also see Lade et al. (1998)], the average of which was about 0.6—with about 80% of spheres in single stagger packing, and the remaining 20% in double stagger packing.

Maximum and minimum void ratios and median grain size of granular soils: their importance and correlations with material properties Das, B.M., Sivakugan, N., Atalar, C.

39

Next we consider the packing of two types of spheres (binary packing) with two different diameters (D = diameter of larger spheres and d = diameter of smaller spheres). Figure 2 shows a schematic diagram of the theoretical variation of the minimum void ratio in a binary packing arrangement (for small D/d ratios). It has primarily two stages:

1. Stage AB—When the volume of small spheres is zero, the minimum void ratio of the primary fabric (larger spheres) is e1. With the increase in the percent of small spheres by volume, the void space of the primary fabric is filled with smaller spheres reaching the lowest point B. This is the filling of the void stage. At point B, the void ratio of smaller spheres is e2, and the minimum void ratio of the larger and small spheres combined is emin(T).

2. Stage BC—Beyond point B, if additional smaller spheres are added, they will replace the larger spheres. At point C, when the percent of smaller spheres is 100% by volume, the minimum void ratio is e2. This phase is called replacement of smaller spheres.

At point B, assuming that the specific gravity of solids of large and small spheres is the same, it can be shown that

2

21

1

1

21

)Tmin(

e

nn

e

n

nne

(2)

where e1, n1 = respectively, minimum void ratio and porosity of larger spheres (point A) e2, n2 = minimum void ratio and porosity, respectively, of smaller spheres (point C)

Figure 2. Variation of minimum void ratio emin in binary packing.

Thus, percent of smaller spheres at B is given by

)100()100(

)(

spheres of weight total

spheressmaller of weight

2

)Tmin(

2

21

1

1

2

21

e

e

e

nn

e

n

e

nn

VT

(3)

In obtaining Eqs. (2) and (3), it is assumed that small spheres can pass through the openings in the void between the larger spheres. As mentioned before, McGeary (1961) observed e1 ≈ e2 ≈ 0.6 (for single spheres). Thus, n1 = n2 = 0.375. Using these values in Eqs. (2) and (3),



40

164.0

6.0

)375.0(

6.0

375.0

)375.0(2

2

2

21

1

1

21

)Tmin(

e

nn

e

n

nne (4)

and percent of smaller spheres of fines,

%2.27)100(

6.0

)375.0(

6.0

375.06.0

)375.0(

)100(2

2

2

21

1

1

2

21

e

nn

e

n

e

nn

VT

(5)

McGeary (1961) also conducted some laboratory tests with two different sizes of steel spheres. The larger spheres had a diameter of 3.15 mm (D). The diameters of the small spheres (d) varied from 0.91 mm to 0.16 mm. This provided D/d ratios varying from 3.46 to 19.69. The minimum void ratios of binary packing thus obtained for D/d = 3.46 and 4.77 is shown in Figure 3. The approximate values of emin(T) and VT as defined in Figure 2 are given in Table 1 and are also plotted in Figure 4. It can be seen that, for D/d ≥ 7, the magnitudes of emin(T) and VT are approximately constant with emin(T) ≈ 0.2 and VT ≈ 27%. These values are not too far off from those calculated in Eqs. (4) and (5).

Figure 3. Variation of emin vs. percent of smaller Figure 4. Variation of emin(T) and VT with D/d steel spheres (based on McGeary 1961). (based on McGeary, 1961).

Table 1. Interpolated values of emin(T) and VT from

binary packing obtained from McGeary’s tests (1961)

D/d emin(T) VT (%)

3.46 4.77 6.56

11.25 16.58 19.69

0.425 0.344 0.256 0.216 0.213 0.192

41.3 26.2 25.0 27.5 26.3 27.5

3 BEHAVIOR OF TWO NATURAL SOIL MIXTURES

The concept presented above for the variation of void ratio of binary mixtures of steel spheres has been compared with the behavior of mixtures of two soils (i.e., mixture of poorly graded sand, and non-plastic fines) by Lade et al. (1998). Two types of poorly graded sand (Nevada sand 50/80 and


41

80/200) were used. The median grain size (D50) of Nevada sand 50/80 was 0.211 mm and that of Nevada sand 80/200 was 0.120. The median grain size (d50) of Nevada non-plastic fines was 0.050. Figure 5 shows the variation of emax and emin with percent of fines for the two binary mixtures. The general trend is similar to that shown in Figure 3. It is important to note that, in Nevada 50/80 sand and fine mixture, the zone of filling the void is clearly seen, and the replacement of larger particles starts when the fine percent reaches about 30% (D50/d50 = 4.2). These two phases are not clear for Nevada 80/200 sand and fine mixtures (D50/d50 = 2.4) since the fine grains do not fit as well between the void spaces present in the sand (Nevada 80/200) compared to those with higher D50/d50 (i.e., Nevada 50/80 and fines). The change in the packing mode in granular soils (i.e. from filling the void to replacement of larger particles) can also be seen from a plot of emax – emin vs. Fc (% of fines). Figure 6 shows a plot for several granular soils (Cubrinovski and Ishihara 2002). The average plot of Fc ≤ 30% is given by the relationship

(%)0087.043.0minmax c

Fee (6)

Equation (6) is generally related to filling the void zone. If Fc > 30% it becomes the zone of replacement of larger particles and thus the slope of the average plot changes. Or,

(%)004.057.0minmax c

Fee (7)

Figure 5. Variation of emax and emin with Figure 6. Variation of emax – emin of sand with fine contents percent of fines (Lade et al. 1998). (based on Cubrinovski and Ishihara, 2002).

4 EFFECT OF GRAIN SHAPE ON emax AND emin Grain shape of natural clean sand has an effect on the maximum and minimum void ratios. The

shape of particles can be expressed by a term called roundness (R) which can be defined as

sphere inscribed maximum theof radius

edges and corners of radius averageR (8)

Figure 7 shows the approximate values of R for various particle shapes. Youd (1973) provided relationships of emax and emin as functions of R and uniformity coefficient Cu (=D60/D10; where D60 and D10 are the diameters through which 60% and 10% of soil passes through, respectively). These are shown in Figures 8 and 9 and are suggested to be valid with normal to moderately skewed grain-size distribution.



42

Figure 7. Definition of roundness R (Youd, 1973).

Figure 8. Variation of emax with Cu and R Figure 9. Variation of emin with Cu and R (Youd, 1973). (Youd, 1973).

Figure 10. Comparison of emax vs. R.

Shimobe and Moreto (1995) have determined the variation of emax with R for 40 uniform clean sand samples having a uniformity coefficient Cu ≤ 2. The experimental range of emax with R is shown in Figure 10. The average plot can be expressed as

354.0

max642.0 Re (9)

Also shown in Figure 10 is the variation predicted by Figure 8 for Cu = 2 which falls below the

average line [i.e. Eq. (9)] and close to the lower limit of the test results by Shimobe and Moreto


43

(1995). It is obvious from the test results that the predicted values of emax can vary over a wide range

since roundness is not an exact quantity. Miura et al. (1997) conducted an extensive study of the physical characteristics of about 200 samples of granular material which included mostly clean sand, some glass beads, and lightweight aggregates (L.W.A.). The grain shape was represented by a quantity called two-dimensional angularity (A2D) Lees (1964a, 1964b) which is an alternative to roundness. Referring to Figure 11,

r

x)180(Angularity (10)

and

angularity2

D

A (11)

To determine A2D of a soil sample, the following procedure was used by Miura et al. (1997).

1. Consider about 20 sand grains having the size of about D50 (medium grain size) from each sample.

2. Obtain enlarged photographic images of the grains taken in the vertical direction. 3. Determine A2D for each projection with the aid of Figure 12. 4. Calculate the average value of A2D for the soil.

Figure 11. Definition of angularity.

Figure 12. Angularity, A2D, estimation chart (Lees, 1964a and 1964b).

Figure 13 shows the results of the study of Miura et al. (1997) in the form of a plot of emax – emin versus A2D that shows three representative linear relationships: (a) for D50 < 0.3 mm, (b) 0.3 mm ≤ D50 < 0.6 mm, and (c) D50 ≥ 0.6 mm. The slope of these lines increases with the decrease in D50 indicating that, for similar values of A2D, the range of emax – emin is higher for fine sand. This also confirms the fact that, for a given value of D50, a decrease in angularity is also accompanied by a decrease in emax – emin.



44

Figure 13. Variation of emax – emin with A2D and D50 (after Miura et al. 1997).

5 CORRELATIONS BETWEEN emax AND emin

Figure 14 shows a plot of emax and emin with median grain size (D50) for clean sand as reported by Miura et al. (1997). The minimum and maximum void ratios show a general tendency to decrease with the increase of median grain size. Based on the details shown in Figure 14, Figure 15 shows a plot of emax versus emin. A regression analysis gives

minmax

62.1 ee (12)

Figure 14. Variation of emax and emin with D50 for Figure 15. Plot of emax and emin from Figure 14 clean sand (Miura et al. 1997). (Miura et al. 1997).


45

Cubrinovski and Ishihara (2002) analyzed a large number of clean sand samples (fine fraction with grain size less than 0.075 mm, Fc ≤ 5%). Based on this analysis they suggested the following relationship

minmax

53.1072.0 ee (13)

The data points upon which Eq. (13) is based and an additional 55 data points for clean sand given by Patra et al. (2010) are shown in Figure 16. From this figure it appears that Eq. (12) may be taken as a good average approximation. The difference in the angularity or roundness of the particles of different soils is another major factor causing the scatter.

Figure 16. Plot of emax vs. emin for clean sand.

Based on best-fit linear regression lines, Cubrinovski and Ishihara (2002) also provided the following relationships for other soils.

Sand with fines (5 < Fc ≤ 15%)

minmax

37.125.0 ee (14)

Sand with fines and clay (15 < Fc ≤ 30%; Pc = 5% to 20%)

minmax

21.144.0 ee (15)

Silty soils (30 < Fc ≤ 70%; Pc = 5% to 20%)

minmax

32.144.0 ee (16)

where Fc = fine fraction for which grain size is smaller than 0.075 mm Pc = clay-size fraction (< 0.005 mm)

6 CORRELATIONS BETWEEN emax – emin AND MEDIAN GRAIN SIZE, D50

Based on a very large database, Cubrinovski and Ishihara (1999, 2002) developed a unique relationship. The database included results from clean sand, sand with fines, and sand with clay, silty soil, gravelly sand, and gravel. This relationship is shown in Figure 17. In spite of some scatter, the average line can be given by the relation,



46

(mm)

06.023.0

50

minmaxD

ee (17)

It appears that the upper and lower limits of emax – emin vs. D50 as shown in Figure 17 can be

approximated as

Lower limit

(mm)

045.016.0

50

minmaxD

ee (18)

Upper limit

(mm)

079.029.0

50

minmaxD

ee (19)

Figure 17. Correlation between emax – emin and D50 (after Cubrinovski and Ishihara, 1999, 2002)

The approximate ranges of emax – emin for clean sand and silty sands are given in Table 2.

Table 2. Range of emax – emin for sandy soils

Soil Fines (%) Gravel (%) emax – emin Clean sand Silty sand Silty sand Silty sand

<5 5 – 10 10 – 20 20 – 30

<5 <5 <5 <5

0.25 – 0.45 0.45 – 0.55 0.5 – 0.6 0.6 – 0.7

Based on the preceding review it appears that there are several factors such as uniformity coefficient, angularity, grain size distribution, and fine contents that affect the maximum and minimum void ratios of granular soils. However, the stress-strain relationships, compressibility, and other practical geotechnical parameters of granular soils can be reasonably predicted from emax – emin, but not separately from emax and/or emin. In spite of some scatter, which is to be expected, emax – emin bears a unique relationship with the median grain size (D50). Hence D50 can be used as a parameter to approximately predict correlation of volumetric strain, relative density, compaction characteristics, strength, and other geotechnical properties of granular soils. Some examples of this are given in the following sections.


47

7 VOLUMETRIC STRAIN POTENTIAL

The volumetric strain potential (v) is the volumetric strain that a granular soil will undergo when it

is densified and the void ratio changes from emax to emin, or

min

minmax

1 e

eev

(20)

A similar parameter like volumetric strain potential was also proposed by Terzaghi [in

Erdbaumechanik (Terzaghi, 1925); also see Bjerrum et al. (1960)] which was referred to as

compactibility (C), or

min

minmaxlitycompactibie

eeC

(21)

Volumetric strain potential will have significant influence on liquefaction of granular soils. Based on the results of Cubrinovski and Ishihara (2002) and Patra et al. (2010), the volumetric strain potential of several sands is shown in Figure 18. The average plot is practically linear. With a variation of about ±10 to 15%, the volumetric strain potential can be expressed as

11)(22(%)minmax

eev

(22)

Combining Eqs. (17) and (22), we obtain

11(mm)

32.106.5(%)

50

D

v (23)

Figure 18. Plot of v vs. emax – emin.



48

8 CORRELATION BETWEEN RELATIVE DENSITY OF CLEAN SAND WITH D50 AND

COMPACTION ENERGY Patra et al. (2010) conducted Proctor compaction tests on 55 clean sand samples—most of which were poorly graded. They also determined emax and emin based on ASTM test procedures given in D-4253 and D-4254. The compaction tests included standard Proctor tests (compaction energy, E = 600 kN-m/m

3), reduced standard Proctor tests with 15 standard Proctor hammer blows per layer (E

= 360 kN-m/m3), modified Proctor tests (E = 2700 kN-m/m

3), and reduced modified Proctor tests

with 12 Proctor hammer blows per layer (E = 1300 kN-m/m3).

Based on the laboratory tests, it has been shown that emax, emin, and void ratio at maximum density

of compaction are as follows:

)7623.0(6042.0 2304.0

50max rDe (24)

)8516.0(3346.0 2491.0

50min rDe (25)

)8040.0(4484.0 2356.0

50 rDe

s (26)

)8095.0(3825.0 204.0

50 rDe

m (27)

)7809.0(5039.0 2327.0

50 rDe

rs (28)

)8076.0(4087.0 2389.0

50 rDe

mr (29)

where D50 is in mm, and es = void ratio from standard Proctor tests, ers= void ratio from reduced standard Proctor tests, em = void ratio from modified Proctor tests, and erm = void ratio from reduced modified Proctor tests The maximum relative density of compaction can then be correlated to the energy of compaction (Patra et al. 2010) as,

B

rADD

50 (30)

where

850.0ln216.0 EA (31)

306.0ln03.0 EB (32)

In Eq. (30), Dr is in fraction, and D50 is in mm. Figure 19 shows a comparison of the relative densities predicted by Eqs. (30)–(32) and those obtained from laboratory tests.


49

Figure 19. Comparison of Dr predicted from Eqs. (30)–(32) with the experimental results (Patra et al. 2010).

9 CORRELATIONS BETWEEN RELATIVE DENSITY (Dr), D50, AND STANDARD

PENETRATION NUMBER (N)

The field standard penetration number in granular soils, N, varies with the effective overburden pressure, o . It can be normalized to a standard effective overburden pressure of 98 kN/m

2 (≈

atmospheric pressure) as (Liao and Whitman, 1986)

5.0

21)(kN/m

98

o

NN (33)

where N1 = normalized standard penetration number Figure 20 shows a correlation between

2

1 / rDN and emax – emin provided by Cubrinovski and Ishihara (1999) which is based on high quality undisturbed samples of silty sand, clean sand, and gravels recovered from natural soil deposits. The average plot shown in Figure 20 can be expressed as

7.1

minmax

2

1

)(

9

eeD

NC

r

D

(34)

Hence

5.0

7.1

minmax

1 )(9

ee

ND

r (35)

Now, combining Eqs. (17), (33) and (35),



50

5.07.1

50 98

9

06.023.0

o

r

DN

D (36)

Figure 20. Development of Eq. (34) (Cubrinovski and Ishihara, 1999).

It is important to note that the N value referred to in Eqs. (34)‒(36) approximately relates to an average energy ratio of 78% for the SPT tests. Figures 21 and 22 show comparisons between Dr predicted using Eq. (34) with that measured, respectively, for gravelly and sandy soils. Kulhawy and Mayne (1990) also provided the following relationship to estimate Dr in which D50 is a factor, or

Figure 21. Measured Dr vs. Eq.(34) for gravel Figure 22. Measured Dr vs. Eq.(34) for sandy

deposits (Cubrinovski and soil deposits (Cubrinovski and

Ishihara, 1999) Ishihara, 1999)


51

5.0

OCR50

601

)log2560(

)(

CCD

ND

A

r (37)

where D50 = median grain size, in mm (N1)60 = normalized standard penetration number for an energy ratio of 60%

100

yearslog05.02.1effect agingfor factor

tC

A (38)

8.1

OCR OCRidationoverconsolfor factor C (39)

where OCR = overconsolidation ratio

10 CORRELATIONS OF CONE PENETRATION TEST RESULTS WITH D50

Based on the results of a large number of cone penetration tests, Anagnostopoulos et al. (2003) have provided a correlation of friction ratio, Rf, with the median grain size, or

cone) (electric)log(36.145.1(%)50

DRf

(40)

cone) l(mechanica)log(6111.17811.0(%)50

DRf

(41)

where D50 is in mm, and

)100((%)c

c

fq

fR (42)

where fc = frictional resistance of sleeve located above the cone qc = cone penetration resistance The plot of Rf versus D50 from which Eqs. (40) and (41) were developed is shown in Figure 23.

Figure 23. Plot of Rf vs. D50 (after Anagnostopoulos, 2003).



52

11 CORRELATION BETWEEN CONE PENETRATION RESISTANCE (qc), STANDARD

PENETRATION RESISTANCE (N60) AND D50

The cone penetration resistance (qc), field standard penetration resistance (N60), and the median grain

size (D50) have been correlated by several investigators in the past. These correlations can be

expressed in a general form as

aa

c

cDN

p

q

50

60

(43)

where D50 is in mm and pa = atmospheric pressure with the same units as qc

Results of some of these studies are summarized below.

Burland and Burbidge et al. (1985)

305.0

50

60

8DN

p

q

a

c

(see Figure 24a) (44)

Based on the data of Robertson and Campanella (1983) and Seed and de Alba (1986)

228.0

50

60

6DN

p

q

a

c

(see Figure 24a) (45)

Figure 24. Continued.


53

Figure 24. Variation of (qc /N60) with D50. (a) Adapted from Terzaghi et al.

(1996); (b) Adapted from Anagnostopoulos (2003); (c) Adapted from

Kulhawy and Mayne (1990).

Based on the data of Anagnostopoulos et al. (2003)

26.0

50

60

6429.7 DN

p

q

a

c

(see Figure 24b) (46)

Based on Kulhawy and Mayne (1990)

288.0

50

60

44.5 DN

p

q

a

c

(see Figure 24c) (47)

12 CONCLUSIONS A review of the various parameters controlling the magnitudes of maximum and minimum void ratios of sandy soils is presented. The magnitudes of emax and emin are primarily functions of uniformity coefficient, angularity, and fine contents. Based on the available results in the literature,



54

the relationships between emax and emin for soils with various percentages of fine contents are included. Also the experimental results suggest that emax – emin (but not emax and emin separately) control the primary geotechnical properties of granular soil, such as volumetric strain potential (v), relative density (Dr), cone penetration resistance (qc), and standard penetration number (N). In spite of some scatter, the median grain size (D50) is probably the best parameter for correlation with emax – emin and, hence, the geotechnical properties related to strength and compression. Also provided in this paper are some correlations presently available in literature between D50 and Dr, v, and qc /N60.

REFERENCES American Society for Testing and Materials (2010), “Annual Book of ASTM Standards,” Sec. 4, Vol. 04.08,

West Conshohocken, Pa. Anagnostopoulos, A., Koukis, G., Sabatakakis, N. and Tsiambaos, G. (2003), “Empirical correlation of soil

parameters based on cone penetration tests (CPT) for Greek soils,” Geotechnical and Geological Engineering, 21(4), 377-387.

Bjerrum, L., Casagrande, A., Peck, R. and Skempton, A.W. (1960), “From Theory to Practice in Soil Mechanics,” John Wiley & Sons, New York, 146-148.

Burland, J.B. and Burbidge, M.C (1985)., “Settlement of foundations on sand and gravel,” Proceedings, Institute of Civil Engineers, Part I, 7, 1325-1381.

Cubrinovski, M. and Ishihara, K. (1999), “Empirical correlation between SPT N-value and relative density for sandy soils,” Soils and Foundations, 39(3), 61-71.

Cubrinovski, M. and Ishihara, K. (2002), “Maximum and minimum void ratio characteristics of sands,” Soils and Foundations, 42(6), 65-78.

Graton, L.C. and Fraser, H.J. (1935), “Systematic packing of spheres—with particular relation to porosity and permeabilitiy,” Journal of Geology, 43(8), 785-909.

Japanese Geotechnical Society (2000), “Test methods for minimum and maximum densities of sands,” Soil Testing Standards, 136-138 (in Japanese).

Kulhawy, F.H. and Mayne, P.W. (1990), “Manual on Estimating Soil Properties for Foundation Design,” Final Report (EL-6800) submitted to Electric Power Research Institute (EPRI), Palo Alto, California.

Lade, P.V., Liggio, C.D. and Yamamuro, J.A. (1998), “Effect of non-plastic fines on minimum and maximum void ratios of sand,” Geotechnical Testing Journal, ASTM, 21(4), 336-347.

Lees, G. (1964a), “The measurement of particle shape and its influence in engineering materials,” Journal of British Granite and Whinestone Federation, 4(2).

Lees, G. (1964b), “A new method for determining the angularity of particles,” Sedimentology, 3. Liao, S. and Whitman, R.V. (1986), “Overburden correction factor for STP in sand, Journal of Geotechnical

Engineering, ASCE,, 112(3), 373-377. McGeary, R.K. (1961), “Mechanical packing of spherical particles,” Journal of the American Ceramic Society,

44(10), 513-522. Miura, K., Maeda, K., Furukawa, M. and Toki, S. (1997), Physical characteristics of sands with different

primary properties,” Soils and Foundations, 37(3), 53-64. Patra, C.R., Sivakugan, N., Das, B.M. and Rout, S.K. (2010), “Correlations for relative density of clean sand

with median grain size and compaction energy,” International Journal of Geotechnical Engineering, 4(2), 195-203.

Robertson, P.K. and Campanella, R.G. (1983), “Interpretation of cone penetration tests. part I: sand,” Canadian Geotechnical Journal, 20(4), 718-733.

Seed, H.B. and DeAlba, P. (1986). “Use of SPT and CPT tests for evaluating the liquefaction resistance of sands.” Proceedings, ASCE Specialty Conference on Use of In Situ Testsing in Geotechnical Engineering, Geotechnical Special Publication 6, Blackburg, 281-302.

Shimobe, S. and Moreto, N. (1995), “A new classification for sand liquefaction,” Proceedings, 1st International

Conference on Earthquake Geotechnical Engineering, Tokyo, 1, 315-320. Terzaghi, K. (1925), “Erdbaumechanik auf Bodenphysikalisher Grundlage,” Deuticke, Vienna, 10-13. Terzaghi, K., Peck, R.B. and Mesri, G. (1996), “Soil Mechanics in Engineering Practice,” 3

rd Ed., John Wiley

& Sons, New York. White, H.E. and Walton, S.F. (1937), “Particle packing and particle shape,” Journal of the American Ceramic

Society, 20(5), 155-166. Youd, T.L. (1973), “Factors controlling maximum and minimum densities of sands,” Evaluation of Relative

Density and Its Role in Geotechnical Projects Involving Cohesionless Soils (STP 523), ASTM, Philadelphia, 98-122.

maximum and minimum void ratios and median grain size of

Documents