INDEX AND CLASSIFICATION PROPERTIES OF SOILS

CHAPTER 2

INDEX AND CLASSIFICATION PROPERTIES OF SOILS

2-1. From memory, draw a phase diagram (like Fig. 2.2, but don’t look first!). The “phases” have a Volume side and Mass side. Label all the parts.

SOLUTION: Refer to Figure 2.2.

2-2. From memory, write out the definitions for water content, void ratio, dry density, wet or mois t density, and saturated density.

SOLUTION: Refer to Section 2.2.

2-3. Assuming a value of ρs = 2.7 Mg/m 3 , take the range of saturated density in Table 2.1 for the six soil types and calculate/estimate the range in void ratios that one might expe ct for these soils.

SOLUTION: Create a spreadsheet using input values from Table 2.1 and Eq. 2.18.

ρ' - minρ' - max e max e min (Mg/m 3 )(Mg/m 3 )

0.9 1.4 0.89 0.21

0.4 1.1 3.25 0.55

1.1 1.4 0.55 0.21

0.9 1.2 0.89 0.42

0.0 0.1

∞ 16.00

0.3 0.8 4.67 1.13

(Given)(see Eq. 2.18)© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.An Introduction to Geotechnical Engineering 2e Robert Holtz William Kovacs Thomas Sheahan (Solutions Manual All Chapters, 100% Original Verified, A+ Grade) No SM Is Provided For Ch 1 and 3 1 / 4

Index and Classification Properties of Soils Chapter 2

2-4. Prepare a spreadsheet plot of dry density in Mg/m 3 as the ordinate versus water content in percent as the abscissa. Assume ρs = 2.65 Mg/m 3 and vary the degree of saturation, S, from 100% to 40% in 10% increments. A maximum of 50% water content should be adequate.

SOLUTION: Solve Eq. 2.12 and Eq. 2.15 for ρ

d = f(ρ s, w, S, Gs), or use Eq. 5.1.ρS w ρ= dry ρ w w+ S ρ s

S = 100 90 80 70 60 50 40 30 20 10

w ρ dry ρ dry ρ dry ρ dry ρ dry ρ dry ρ dry ρ dry ρ dry ρ dry (%) (Mg/m 3 )(Mg/m 3 )(Mg/m 3 )(Mg/m 3 )(Mg/m 3 )(Mg/m 3 )(Mg/m 3 )(Mg/m 3 )(Mg/m 3 )(Mg/m 3 )

0.0 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65

5.0 2.34 2.31 2.27 2.23 2.17 2.09 1.99 1.84 1.59 1.14

10.0 2.09 2.05 1.99 1.92 1.84 1.73 1.59 1.41 1.14 0.73

15.0 1.90 1.84 1.77 1.69 1.59 1.48 1.33 1.14 0.89 0.53

20.0 1.73 1.67 1.59 1.51 1.41 1.29 1.14 0.96 0.73 0.42

25.0 1.59 1.53 1.45 1.36 1.26 1.14 1.00 0.83 0.61 0.35

30.0 1.48 1.41 1.33 1.24 1.14 1.02 0.89 0.73 0.53 0.30

35.0 1.37 1.31 1.23 1.14 1.04 0.93 0.80 0.65 0.47 0.26

40.0 1.29 1.22 1.14 1.05 0.96 0.85 0.73 0.58 0.42 0.23

45.0 1.21 1.14 1.06 0.98 0.89 0.78 0.67 0.53 0.38 0.21

50.0 1.14 1.07 1.00 0.92 0.83 0.73 0.61 0.49 0.35 0.19

Problem 2-4 0.00 0.50 1.00 1.50 2.00 2.50 3.00

0 5 10 15 20 25 30 35 40 45 50 55

w (%) ρ dry (Mg/m3 )

S=100%

S=90% S=80% S=70% S=60% S=50% S=40% S=30% S=20% S=10%© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. 2 / 4

Index and Classification Properties of Soils Chapter 2

2-5a Prepare a graph like that in Problem 2.4, only use dry density units of kN/m 3 and pounds per cubic feet.

SOLUTION:

ρS w

From Eq. 2.12 and Eq. 2.15: ρ=

dry ρ w w+ S ρ s

S = 100 90 80 70 60 50 40 30 20 10

w γ dry γ dry γ dry γ dry γ dry γ dry γ dry γ dry γ dry γ dry (%) (kN/m 3 )(kN/m 3 )(kN/m 3 )(kN/m 3 )(kN/m 3 )(kN/m 3 )(kN/m 3 )(kN/m 3 )(kN/m 3 )(kN/m 3 )

0.0 26.00 26.00 26.00 26.00 26.0026.00 26.00 26.00 26.00 26.00

5.0 22.95 22.66 22.30 21.86 21.2920.55 19.53 18.03 15.64 11.18

10.0 20.55 20.08 19.53 18.86 18.0316.99 15.64 13.80 11.18 7.12

15.0 18.60 18.03 17.37 16.58 15.64 14.48 13.04 11.18 8.70 5.23

20.0 16.99 16.36 15.64 14.79 13.80 12.62 11.18 9.40 7.12 4.13

25.0 15.64 14.97 14.22 13.36 12.35 11.18 9.79 8.10 6.03 3.41

30.0 14.48 13.80 13.04 12.17 11.18 10.04 8.70 7.12 5.23 2.90

35.0 13.49 12.80 12.04 11.18 10.21 9.11 7.83 6.35 4.61 2.53

40.0 12.62 11.94 11.18 10.34 9.40 8.33 7.12 5.73 4.13 2.24

45.0 11.86 11.18 10.44 9.62 8.70 7.68 6.53 5.23 3.73 2.01

50.0 11.18 10.52 9.79 8.99 8.10 7.12 6.03 4.80 3.41 1.82

Problem 2-5a 0.00 5.00 10.00 15.00 20.00 25.00 30.00

0 5 10 15 20 25 30 35 40 45 50 55

w (%) γ dry (kN/m3 )

S=100%

S=90% S=80% S=70% S=60% S=50% S=40% S=30% S=20% S=10%© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. 3 / 4

Index and Classification Properties of Soils Chapter 2

2-5b Prepare a graph like that in Problem 2.4, only use dry density units of pounds per cubic feet.

SOLUTION:

sw dry s GS SGw γ γ= +

S = 100 90 80 70 60 50 40 30 20 10

w γ dry γ dry γ dry γ dry γ dry γ dry γ dry γ dry γ dry γ dry (%) (pcf) (pcf) (pcf) (pcf) (pcf) (pcf) (pcf) (pcf) (pcf) (pcf)

0.0 165.36 165.36 165.36 165.36 165.36 165.36 165.36 165.36 165.36 165.36

5.0 146.01 144.14 141.86 139.04 135.45 130.72 124.21 114.70 99.46 71.12

10.0 130.72 127.75 124.21 119.95 114. 70 108.08 99.46 87.80 71.12 45.30

15.0 118.33 114.70 110.47 105.47 99.46 92.12 82.94 71.12 55.35 33.24

20.0 108.08 104.07 99.46 94.11 87.8080.27 71.12 59.77 45.30 26.25

25.0 99.46 95.25 90.45 84.96 78.5971.12 62.25 51.54 38.34 21.69

30.0 92.12 87.80 82.94 77.43 71.1263.85 55.35 45.30 33.24 18.48

35.0 85.79 81.44 76.58 71.12 64.9557.92 49.83 40.41 29.33 16.09

40.0 80.27 75.93 71.12 65.77 59.7753.00 45.30 36.48 26.25 14.26

45.0 75.42 71.12 66.39 61.16 55.3548.85 41.53 33.24 23.75 12.79

50.0 71.12 66.89 62.25 57.16 51.5445.30 38.34 30.53 21.69 11.60

Problem 2-5b 0.00 20.00 40.00 60.00 80.00

100.00

120.00

140.00

160.00

180.00

0 5 10 15 20 25 30 35 40 45 50 55

w (%) γ dry (pcf)

S=100%

S=90% S=80% S=70% S=60% S=50% S=40% S=30% S=20% S=10%© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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