Find: Vwater[gal] you need to add S 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,

Find: Vwater[gal] you need to add S 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,

Find: Vwater[gal] you need to add S 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.

Find: Vwater[gal] you need to add S 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 ---

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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 0.8 --- VS 135,000 VS VS VA=VW

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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]

Find: Vwater[gal] you need to add S 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]

Find: Vwater[gal] you need to add S 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]

Find: Vwater[gal] you need to add S 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]

Find: Vwater[gal] you need to add S 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]

Find: Vwater[gal] you need to add S 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]

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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)=

Find: Vwater[gal] you need to add S 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

Find: Vwater[gal] you need to add S 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]

Find: Vwater[gal] you need to add S 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]

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]

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

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

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

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

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

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

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

( ) ? 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