For the concrete Dam shown in figure, determine the total average seepage for the given permeable strata by drawing Flow Net. The detail dimensions are given on the figure. The head of water on upstream side is 6ft and on downstream side is 1ft. Assume of Nf= 3, Nd= 6 and rectangular flow elements.

 

Q#:For the concrete Dam shown in figure, determine the total average seepage for the given permeable strata by drawing Flow Net. The detail dimensions are given on the figure. The head of water on upstream side is 6ft and on downstream side is 1ft. Assume of Nf= 3, Nd= 6 and rectangular flow elements. 

Solution#

 ANSWER 

 SOLUTION

For rectangular channel

n=b/L = 2/4 =0.5

seepage equation for rectangular chanel                                                                           

 

                                                                                                                 k = 4×10^-4 ft/day

q = kH (Nf / Nd)                                                                                       H = h₁ - h₂

                                                                                                                 H = 6-1 = 5

No. of potetial drop = 6                                                                           Nf =  3

No. of Flow lines     = 3                                                                           Nd = 6

H = 6 - 1 = 5'

 

Rate of Seepage

 

 q = nf / nd kh

  

q = 3/6×4×10^-4 × 5

 q = 1×10^-3 ft³ /day/ft

The following are the results of different tests on soil samples are provided in the following table. Soil sample Percent passing sieve Liquid Limit plasticity Index No 10 No 40 No 200 A 100 75 25 35 15 B 100 85 30 45 22 C 80 45 10 25 12 Classify the soil according to AASTHO classification and determine the Group Index in each case. You may use the information provided.

 

Q#3 :The following are the results of different tests on soil samples are provided in the following table.                      

Soil sample	Percent passing sieve			Liquid Limit	plasticity Index
	No 10	No 40	No 200
A	100	75	25	35	15
B	100	85	30	45	22
C	80	45	10	25	12

Classify the soil according to AASTHO classification and determine the Group Index in each case. You may use the information provided.

ANSWER

SOIL Sample  A

      Percentage passing through  No. 10  (2mm) seive = 100%

      Percntage passing  through No. 40 (425 μm) seive = 75%

      Percentage passing through No. 200 (75 μm) seive = 25%

 

              Liquid limit = wL = 35

             Plasticity index = I_p = 15

Percenrage passing through no. 200 seieve  < 35%

        So there for soil is granual

because Percentage passing through no.10 (2mm) seive > 50%

Percentage passing through no. 40 (425 μm) seive > 50%

Percentage passing through no.200(75 μm) >10%  < 35%

There fore soil group is A -2

 Because  wL < 40    and    I_p > 11

 

There fore soil subgroup is A-2-6

 Group index of the soil is given as

GI = 0.2a = 0.005ac +0.01 bd

a = percentage passing through  75 μm seive  -35                     a  ≤  40

b = percentage passing through 75 μm seive  -15                       b ≤  40

c = wL -40        c  ≤  20

d = I_p– 10        d  ≤  20

 

Therefore,

                        a= 25-35= -10

                        b =25-15 =10

                        c = 35-40 = -5

                        d = 15-10 = 5

GI= 0.2 × (-10)+0.005 ×(-10)(-5)+0.01 × (10)(5)

GI = -2+0.25+0.5

GI = -1.5

There is no negative group index of soil is zero

There for soil classified is  A-2-6

 

SOIL Sample  B

      Percentage passing through  No. 10  (2mm) seive = 100%

      Percntage passing  through No. 40   (425 μm) seive = 85%

      Percentage passing through No. 200  (75 μm) seive = 30%    (My reg no.)

 

              Liquid limit = wL = 45

             Plasticity index = I_p = 22

 

Percenrage passing through no. 200 seieve  >35%

        So there for soil is silt clay type

because wL  > 41   and I_p   >  11 

 

There fore soil group is A -7

(wL  - 30) = 45 -30 =15

 Because  and    I_p > (wL  - 30)

There fore soil subgroup is A-7-6

 Group index of the soil is given as

GI = 0.2a = 0.005ac +0.01 bd

a = percentage passing through  75 μm seive  -35                     a  ≤  40

b = percentage passing through 75 μm seive  -15                       b ≤  40

c = wL -40        c  ≤  20

d = I_p– 10        d  ≤  20

 

Therefore,

                        a= 30-35=-5

                        b =30-15 =15

                    

                        c = 45-40 = 5

                        d = 22-10 = 12

GI= 0.2 × (-5) +0.005 × (-5)  ×5 +0.01 × 15 ×12

GI = 0.675

The group index of soil is = 0.675

There for soil classified is  A-7-6(0.675)        (clay soil)

 

SOIL Sample  C

      Percentage passing through  No. 10  (2mm) seive = 80%

      Percntage passing  through No. 40 (425 μm) seive = 45%

      Percentage passing through No. 75 (75 μm) seive = 10%

 

              Liquid limit = wL = 25

             Plasticity index = I_p = 12

 

Percentage passing through no. 200 seieve  < 35%

        So there for soil is granual

because Percentage passing through no.10 (2mm) seive > 50%

Percentage passing through no. 40 (425 μm) seive < 50%

Percentage passing through no.200(75 μm) >10%  < 25%

 

There fore soil subgroup is A-2-6

Group index of the soil is given as

GI = 0.2a = 0.005ac +0.01 bd

a = percentage passing through  75 μm seive  -35                     a  ≤  40

b = percentage passing through 75 μm seive  -15                       b ≤  40

c = wL -40        c  ≤  20

d = I_p– 10        d  ≤  20

 

Therefore,

                        a= 10-35= - 25

                        b =10-15 = -5

                        c = 25-40 = 15

                        d = 12-10 = 2

 

GI= 0.2 × (-25)+0.005 ×(-25)(-15)+0.01 × (-5)(2)

GI = -5+1.875+0.01

GI = -3.135

There for group index of soil is zero

There for soil classified is  A-1-b(0)

Derive and explain Darcy’s Law in light of its application in design of foundation for the discharge of water through the soil sample.

Q#:Derive and explain Darcy’s Law in light of its application in design of foundation for the discharge of water through the soil sample.     

ANSWER

Darcy’s law;

    Darcy’s law states the principle which governs the movement of fluid in the given substance. Darcy’s law equation that describes the capability of the liquid to flow via any porous media like a rock. The law is based on the fact according to which, the flow between two points is directly proportional to the pressure differences between the points, the distance, and the connectivity of flow within rocks between the points. Measuring the inter-connectivity is known as permeability. 

Darcy's law demonstrat experimently that for leminar flow condition in a saturated soil mass,  the velocity of flow is directly proportional to hydraulic gradients

 i.e  V ∝ i

Or   V = ki

Where K is coefficient of permeability

   I is  hydraulic gradient

I =  Δh/ L

Δ h = change in head b.w two observation points.

L= length b.w the two points

Now considering applipcation in the design of foundation the equation for discharge can be derived  from a flow net as

 

Δ q =  k× Δh/ L

Δh = H/Nd where Nd is number of potential drops 

Δ q=  Kh/ L × 1/Nd ×b

Or

Δ q= kH/Nd × (b/L)

 

The total discharge  through flow net will be

I= h₁ -h₂ /L

Or

v=k (h₁  -h₂ ) / L

 Now discharge of water through the soil sample

q=v × area= v×A

or

q= k (h₁-h₂) / L ×L

 

q = Nf × Δ q

= Nf × k H/Nd × b/L

q = kH Nf/Nd × b/L

The field is approximate square b= L

 q = kH Nf/Nd

 

or

Total head = P/w + v²/2g +z

 piezometric head = p/w +z

 In soil mechanics  v²/2g is neglected as  it is very small

 

Flow occurs only when there is difference  in total head b.w 2point 

Total head difference is      H₁ -H₂ =  h_f

                                                          h_f= H_{1 -}H₂ 

 

Total head loss b.w 2 poits in a soil is  equal to the difference in the elevation of water level in the 2 piezometer kept @ those 2 poits

 

Seepage length = L

hydraulic gradient = h/L  (Head loss per unit length)

c/s of section x-x

c/s area of soil  = A = b×d

Mutual area of flow = Av = nA (    AREA of voids)

 discharge velocity/apparent velocity of flow = Q/A

 seepage velocity/ actual velocity Vs = Q/Av

 

Q= AV =Av ×Vs

Vs = A/Av  (v)

 

     Vs = v/n                Vs > V

Charging Backpack

 Backpack, Travel Backpack for Men Women, Laptop Backpack, Lapsouno Extra Large 17 inch School College Bag with USB Port, 40L High Capacity Water Resistant TSA Carry on Computer Business Backpack, Blue

Visit the Lapsouno Stor

e

Color: Blue

 
 
 
 

                    Order Now, Click Here

• 
  
• 【LARGE CAPACITY & MORE STORAGE】:Lapsouno Large Carry On Travel Backpack More than 15 multi-function combination pockets, there are two main block pockets. A separate laptop compact, the maximum can accommodate a 17.3-inch laptop,travel backpack has two mesh compartments suitable for your laptop accessories,multiple compact,allowing your item well,17 Inch Laptop Backpack equivalent to 18-inch trolley case.
• 【COMFORTABLE & DURABLE MULTI-PURPOSE】:This Lapsouno Carry on backpack multi-sided airflow design provides honeycomb back pads, shoulder straps, breathable, adjustable shoulder straps, belt liners, help to relieve the back pressure of shoulders, nd protect your items Free use of any bumps on the road,lasting. This computer backpack has tie rod fixtures, which can be fixed in trolley boxes, Large Carry On Travel Backpack makes your travel easier.
• 【PREMIUM MATERIALS & WATERPROOF ANTI-THEFT DESIGN】:Lapsouno Carry on bag is made of lightweight waterproof polyester and scratch materials, which can be protected in rainy days. The Travel Backpack metal zipper adopts double-sided smooth railing and reinforced sewing, lightweight, rainy day, can provide leak-proof protection for items; the anti-theft zip pocket in the back of the luggage backpack is to protect your valuables,let you take the key,cash,etc Valuable objects.
• 【CONVENIENT USB PORT DESIGN】: Lapsouno Laptop backpack provides convenient portable power supply, and computer backpack is a USB charging port externally, which is very suitable for your mobile phone or other electronic devices.(Please note that the USB port does not include charging lines, you need yourself).As a backpack for men / backpack for women / travel backpack / carry on backpack, you will enjoy It's fashionable and convenient everywhere.
• 【SCIENTIFIC COMFORT BACK ERGONOMICS】:The ergonomic design of this 17-inch college backpack ensures that it can be carried comfortably even with all your gear on. The comfortable and breathable shoulder straps of the anti theft backpack help relieve shoulder pressure. In addition, this computer backpack has a sturdy handle on the top for easy carrying. The Lapsouno Backpack luggage strap can easily attach your large backpack to your luggage, making your travel more convenient.
• 【100% LIFETIME & WARRANTY】:Buy this product to get a lifetime warranty of Lapsouno waterproof laptop backpack and 7*24 hours friendly customer service. Backpack, Laptop Backpack, Carry on Backpack, Durable Extra Large 17 Inch TSA Friendly Business Travel Laptop Backpack with USB Port, Lapsouno Anti Theft College School Bag Gifts for Men Women,you deserve it!
• 【 LARGE COLLEGE BACKPACKS FOR CAMPUS】Lapsouno college backpack is suitable for students and teachers. School College backpack for students.Teachers and students use this work backpack, which can hold a 17.3-inch laptop, making it easy and portable for your journey.school bags is suitable for college students, high school students and middle school students' graduation gifts.teacher backpack women, teacher backpack for men,bookbag for School.

• 【BEST GIFTS -COMPUTER BACKPACK】:A business backpack suitable for work, no problem at all with a 17.3 inch computer.it is a anti theft backpack suitable for leisure hiking.backpack for Father's Day Gifts, backpack for Mother's Day Gifts.Gifts for men, Gifts for women,computer bags for women,computer bags for men,business backpack for men, business backpack for women,Lapsouno Extra Large backpack you deserve it!
• 【TSA 180° OPENING DESIGN】:Lapsouno TSA friendly backpack design. At the security checkpoint, the TSA backpack can be easily opened 180°, making this large notebook aircraft backpack easier to pass the airport security check and have a pleasant and relaxing air travel. In addition, laptop backpack for men, laptop backpack for women and laptop bag have great compatibility.