1. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
780
5,800
43,000
360,000
Find the volume of water, in gallons, you need to add to a quantity of soil to achieve a desired water content. [pause] In this problem,

2. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
780
5,800
43,000
360,000
we’ve been provided certain properties about the soil,

3. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
780
5,800
43,000
360,000
and we’ll use the block diagram to help us solve this problem.

4. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3
780
5,800
43,000
360,000
We begin with the volume side of the diagram and convert ---

5. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3
780
5,800
43,000
360,000
our total volume into cubic feet.
135,000

6. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3
780
5,800
43,000
360,000
Next we consider the saturation,
135,000

7. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VW S=
which is defined as the volume of water divided by the volume of voids. VV
135,000

8. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VW VW S= =
Where the volume of voids is equivalent to the volume of air plus the volume of water, VV
VW+VA
135,000

9. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VW VW S= =
=0.5
and its been given that the saturation is value is 50% or 0.5. VV
VW+VA
135,000

10. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VW VW S= =
=0.5
If we rearrange the equation --- VV
VW+VA
135,000
0.5*(VW+VA)=VW

11. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VW VW S= =
=0.5
we learn the volume of air is equal to the volume of water. VV
VW+VA
135,000
0.5*(VW+VA)=VW
0.5*VW+0.5*VA=VW

12. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VW VW S= =
=0.5
--- VV
VW+VA
135,000
0.5*(VW+VA)=VW
0.5*VW+0.5*VA=VW
0.5*VA=0.5*VW

13. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VW VW S= =
=0.5
--- VV
VW+VA
135,000
0.5*(VW+VA)=VW
0.5*VW+0.5*VA=VW
0.5*VA=0.5*VW
VA=VW

14. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VV e=
Next we’ll look at the void ratio, VS
135,000
VA=VW

15. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VV
VW+VA e= =
which is equal to the volume of voids divided by the volume of solids. VS
135,000 VS
VA=VW

16. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VV
VW+VA e= =
Since the volume of air, equals the volume of water, VS
135,000 VS
VA=VW

17. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VV
VW+VA e= =
we make a substitution, VS
135,000 VS
VA=VW

18. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VV
VW+VW e= =
and simplify. VS
135,000 VS
VA=VW

19. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VV
VW+VW
2*VW e= = =
--- VS
135,000 VS VS
VA=VW

20. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VV
VW+VW
2*VW e= = =
=0.8
We were given the void ratio is VS
135,000 VS VS
VA=VW

21. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VV
VW+VW
2*VW e= = =
=0.8
so we compute the --- VS
135,000 VS VS
VA=VW
2*VW=0.8*VS

22. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VV
VW+VW
2*VW e= = =
=0.8
volume of solid to be 2.5 times the volume of water. VS
135,000 VS VS
VA=VW
2*VW=0.8*VS
2.5*VW=VS

23. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VV
VW+VW
2*VW e= = =
=0.8
--- VS
135,000 VS VS
VA=VW
2*VW=0.8*VS
2.5*VW=VS

24. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3 27
yd3 VV
VW+VW
2*VW e= = =
=0.8
--- VS
135,000 VS VS
VA=VW
2*VW=0.8*VS
VS=2.5*VW
2.5*VW=VS

25. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18% VA
ft3 27
yd3 VW VS VV
VW+VW
2*VW e= = =
=0.8
Since we know the total volume is 135,000 cubic feet, VS
135,000 VS VS
VA=VW
2*VW=0.8*VS
VS=2.5*VW
2.5*VW=VS

26. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18% VA
ft3 27
yd3 VW VS
VT=VA+VW+VS
we can now solve our linear system of equations, of 3 equations and 3 unknowns.
135,000
VA=VW
VS=2.5*VW

27. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18% VA
ft3 27
yd3 VW VS
VT=VA+VW+VS
we begin substituting and solving,
135,000
VA=VW
VS=2.5*VW

28. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18% VA
ft3 27
yd3 VW VS
VT=VA+VW+VS
+++ and determine the volume of water is 30,000 cubic feet.
135,000
135,000=VW
VA=VW
+VW+2.5*VW
VS=2.5*VW

29. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18% VA
ft3 27
yd3 VW VS
VT=VA+VW+VS
---
135,000
135,000=VW
VA=VW
+VW+2.5*VW
VS=2.5*VW
135,000=4.5*VW

30. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18% VA
ft3 27
yd3 VW VS
VT=VA+VW+VS
---
135,000
135,000=VW
VA=VW
+VW+2.5*VW
VS=2.5*VW
135,000=4.5*VW
VW=30,000[ft3]

31. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18% VA
ft3 27
yd3
30,000 VS
VT=VA+VW+VS
Since the volume of water and the volume or air are equal,
135,000
135,000=VW
VA=VW
+VW+2.5*VW
VS=2.5*VW
135,000=4.5*VW
VW=30,000[ft3]

32. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18% VA
ft3 27
yd3
30,000 VS
VT=VA+VW+VS
the volume of air is also,
135,000
135,000=VW
VA=VW
+VW+2.5*VW
VS=2.5*VW
135,000=4.5*VW
VW=30,000[ft3]

33. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3
30,000 27
yd3
30,000 VS
VT=VA+VW+VS
30,000 cubic feet.
135,000
135,000=VW
VA=VW
+VW+2.5*VW
VS=2.5*VW
135,000=4.5*VW
VW=30,000[ft3]

34. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3
30,000 27
yd3
30,000 VS
VT=VA+VW+VS
And the volume of solid,
135,000
135,000=VW
VA=VW
+VW+2.5*VW
VS=2.5*VW
135,000=4.5*VW
VW=30,000[ft3]

35. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
ft3
30,000 27
yd3
30,000
75,000
VT=VA+VW+VS
is 75,000 cubic feet. [pause]
135,000
135,000=VW
VA=VW
+VW+2.5*VW
VS=2.5*VW
135,000=4.5*VW
VW=30,000[ft3]

36. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18% WA
30,000 WW
30,000
75,000 WS
Next we solve for the weights of our three components.
135,000

37. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18% WA
30,000 WW
30,000
75,000 WS
Of course the weight of air here is zero.
135,000

38. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000 WW
30,000
75,000 WS
---
135,000

39. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000 WW
30,000
75,000 WS
WW= γW*VW
The weight of water is the product of the volume of water and unit weight of water.
135,000

40. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000 WW
30,000
75,000 WS
WW= γW*VW
---
135,000 lb
62.4
ft3

41. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000 WS
WW= γW*VW
and equal to 1.87 million pounds.
135,000 lb
62.4
ft3

42. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000 WS
WW= γW*VW
The weight of solid is solved the same way,
135,000 lb
62.4
ft3
WS= γW*SG*VS

43. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000 WS
WS= γW*VW
just a different volume and specific gravity.
135,000 lb
62.4
ft3
WS= γW*SG*VS

44. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000
1.24*107
WS= γW*VW
The weight of the solid is 12.4 million pounds.
135,000 lb
62.4
ft3
WS= γW*SG*VS

45. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000
1.24*107
WS= γW*VW
Which makes the total weight 14.3 million pounds. [pause]
135,000
1.43*107 lb
62.4
ft3
WS= γW*SG*VS

46. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000
1.24*107
Finally, we need to consider the desired water content.
135,000
1.43*107

47. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000
1.24*107
wc= WW WS
The water content is the weight of the water divided by the weight of the solid material.
135,000
1.43*107

48. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000
1.24*107
wc= WW WS
WW+WW(to add)
The weight of water can be thought of as, the water already in the soil plus the water we still need to add to achieve the desired water content. =
135,000
1.43*107 WS

49. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000
1.24*107
wc= WW WS
WW+WW(to add)
Solving for the weight of water we still need to add, =
135,000
1.43*107 WS
WW(to add)=

50. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000
1.24*107
wc= WW WS
WW+WW(to add)
and plugging in our known values, =
135,000
1.43*107 WS
WW(to add)=wc*WS-WW

51. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000
1.24*107
wc= WW WS
WW+WW(to add)
the weight of water we still need to add is 3.62 times 10 to the fifth pounds. =
135,000
1.43*107 WS
WW(to add)=wc*WS-WW
=3.62*105 [lb]

52. Find: Vwater[gal] you need to addS
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000
1.24*107
wc= WW WS
WW+WW(to add)
However, were asked to find the volume of water we need to add. =
135,000
1.43*107 WS
WW(to add)=wc*WS-WW
=3.62*105 [lb]

53. γW Find: Vwater[gal] you need to add A W S wc= Vtotal=5,000[yd3] e=0.8
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000
1.24*107
wc= WW WS
WW+WW(to add)
So, we divide by the unit weight of water, =
135,000
1.43*107 WS
WW(to add)
WW(to add)=wc*WS-WW
VW(to add)= γW
=3.62*105 [lb]

54. γW Find: Vwater[gal] you need to add A W S wc= Vtotal=5,000[yd3] e=0.8
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000
1.24*107
wc= WW WS
WW+WW(to add)
And come up with --- =
135,000
1.43*107 WS
WW(to add)
WW(to add)=wc*WS-WW
VW(to add)= γW
=3.62*105 [lb] lb
62.4
ft3

55. γW Find: Vwater[gal] you need to add A W S wc= Vtotal=5,000[yd3] e=0.8
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000
1.24*107
wc= WW WS
WW+WW(to add)
5,801 cubic feet of water to add. =
135,000
1.43*107 WS
WW(to add)
WW(to add)=wc*WS-WW
VW(to add)= γW
=3.62*105 [lb] lb
=5,801[ft3]
62.4
ft3

56. γW Find: Vwater[gal] you need to add A W S wc= Vtotal=5,000[yd3] e=0.8
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000
1.24*107
wc= WW WS
WW+WW(to add)
Yet the question asks for the units to be in gallons. =
135,000
1.43*107 WS
WW(to add)
WW(to add)=wc*WS-WW
VW(to add)= γW
=3.62*105 [lb] lb
=5,801[ft3]
62.4
ft3

57. γW Find: Vwater[gal] you need to add A W S Vtotal=5,000[yd3] e=0.8
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000
1.24*107
gal
VW(to add)=VW(to add)[ft3] * 7.48
So, after one more conversion our final answer is ---
ft3
135,000
1.43*107
WW(to add)
WW(to add)=wc*WS-WW
VW(to add)= γW
=3.62*105 [lb] lb
=5,801[ft3]
62.4
ft3

58. γW Find: Vwater[gal] you need to add A W S Vtotal=5,000[yd3] e=0.8
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
30,000
1.87*106
75,000
1.24*107
gal
VW(to add)=VW(to add)[ft3] * 7.48
43,394 gallons.
ft3
135,000
1.43*107
= 43,394 [gal]
WW(to add)
WW(to add)=wc*WS-WW
VW(to add)= γW
=3.62*105 [lb] lb
=5,801[ft3]
62.4
ft3

59. γW Find: Vwater[gal] you need to add A W S Vtotal=5,000[yd3] e=0.8
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
780
5,800
43,000
360,000
30,000
1.87*106
75,000
1.24*107
gal
VW(to add)=VW(to add)[ft3] * 7.48
Looking back at our possible solutions,
ft3
135,000
1.43*107
= 43,394 [gal]
WW(to add)
WW(to add)=wc*WS-WW
VW(to add)= γW
=3.62*105 [lb] lb
=5,801[ft3]
62.4
ft3

60. γW Find: Vwater[gal] you need to add A W S Answer: C Vtotal=5,000[yd3]
V [ft3]
W [lb]
Vtotal=5,000[yd3]
e=0.8
SG=2.65
S=50%
wcdesired=18%
30,000
780
5,800
43,000
360,000
30,000
1.87*106
75,000
1.24*107
gal
VW(to add)=VW(to add)[ft3] * 7.48
the answer is C.
ft3
135,000
1.43*107
= 43,394 [gal]
Answer: C
WW(to add)
WW(to add)=wc*WS-WW
VW(to add)= γW
=3.62*105 [lb] lb
=5,801[ft3]
62.4
ft3

62. ( ) ? τ [lb/ft2] γclay=53.1[lb/ft3] Index σ’v = Σ φ γ Δ d ˚ H*C σfinal
wc= WW WS 1
Index
γclay=53.1[lb/ft3]
Find: σ’v ρc d = 30 feet
(1+wc)*γw
wc+(1/SG)
σ’v = Σ φ γ Δ d ˚ d
Sand
10 ft
γT=100 [lb/ft3]
100 [lb/ft3]
φ=α1-α2
10 [ft]
20 ft
Clay
= γsand dsand
+γclay dclay A W S
V [ft3]
W [lb]
40 ft
text
wc = 37% ? Δh
20 [ft]
τ [lb/ft2]
62.4 lb
ft3 27
yd3
ft3
(5 [cm])2 * π/4
( )
H*C σfinal
ρcn=
1+e σinitial
log ‘ φ
size[mm]
% passing 0%
20%
40%
60%
80%
100% 10 1
0.1
0.01
c=0
400
1,400 σ3
Sand σ1