Soil & Water Conservation Structures 3(2+1)

Lesson 18. Structural Design of Drop Spillway-II

18.1 Design Example

Design the structure of a straight inlet drop spillway with a straight apron outlet, to be installed for gully control. The expected peak runoff rate through the gully is 5.83 m³/s. For dimension of the structure refer example 16.1. Assume fill condition for the design.

Soil

• Angle of internal friction = 25^o

• Cohesion resistance = 500 Kg/m³

• Unit weight of soil = 1900 Kg /m³

Brick

• Unit weight of masonry = 1900 Kg /m³

 Foundation

• Made of firm clay. Its creep ratio, C_w = 2.3

 Water

• Unit weight of water = 1000 Kg/m³

 Solution:

From example 16.1              

The crest length of weir, L = 4.0 m

          and                       h = 0.97 m

Apron length,                   L_b= 3.25 m

Cutoff wall / toe wall = 0.567 m = 0.57 m

Total uplift pressure head = F = 2 m

 

Analysis of forces

Forces	Volume of component (m3)	Material Density (Kg/m3)	Force/unit length of structure (Kg/m)	Lever arm length (m)	Moment kg	Type of moment
P1	2 x 0.97 x 1	1000 (water)	1940	At 0.5 x 2 = 1.0 from base	1940	overturning
P2and P3	0.5 x 2 x 2 x 1	1000 (water), 1900 (soil)	2000+3800 =5800	At 1/3 x 2 = 0.66 from base	3862.8	Overturning
Pu1	(0.5 x 1.43 x 4.75) x 1	1000 (water)	3396.25	At 2/3 x 4.75 = 3.16 from toe	10754.8	Overturning
Pu2	0.57 x 4.75 x 1	1000 (water)	2707.5	At 0.5 x 4.75 = 2.375	6430. 31	Overturning
Total overturning moment						22987.91
W1	2 x 1 x 1	2100 (Bick masonry)	4200	At 4.75 – 0.5 4.25 from toe	17850	Restoring
W2	0.5 x 2 x 1 x 0.5	2100 (Brick masonry)	1050	At 3.25 + (2/3) x 0.5 = 3.55 from toe	3762.5	Restoring
W3	4.75 x 0.57 x 1	2100 (Brick masonry)	5685.75	At 0.5 x 4.75 = 2.375 from toe	13503.65	Restoring
Total restoring moment						35116.15

 

Safety against Overturning: For safety against overturning,

Total restoring moment > Total overturning moment

i.e.,               

 

Therefore, the structure designed is safe against overturning.

Safety against Sliding: For safety against sliding, ΣH shouldn’t be greater than f.ΣV + CA, where horizontal forces, H= P₁ +P₂+ P_3, Vertical forces, V = W₁ +W₂ + W₃ – P_u1 –P_u2, and f = tan ѳ(angle of internal friction of soil), C is the cohesion resistance of soil, and A = area of the plane of sliding.

ΣH = 1940 + 5800 = 7740 kg/m

ΣV = 4200+1050+5685.75 – (3396.25+2707.5) = 4832 kg/m

fΣV + CA = 0.466 x 4832 + 500 x 4.75 x 2 =7001.712 kg/m

 As this is greater than ΣH, the structure is safe against sliding.

 

Safety against Tension

Assuming restoring moments as positive and turning moments as negative, the value of z is calculated as:

          z = ΣH/ΣV

             = (35116.15- 22987.91) / 4832 = 2.50

          e = 2.50 – (4.75/2) = 0.125 m

width (d)/6 = 4.75/6 = 0.791 m

 

This shows that, e = 0.125 is less than 0.791 and structure is therefore safe against tension.

 

Safety against Compression

For safety against compression, the forces should be compressive in nature, so that there is no floatation of the structure.

Contact pressure,

                            

                                      = 1017.26 +160.62 Kg / m²

                                      = 1177.9 Kg / m²at upstream side

                          =856.64 Kg / m²at downstream side

Hence the resultant pressure is downward and, therefore the structure is safe against compression.

Safety against Piping

For safety against piping, the weighted creep ratio C_w should be higher than the recommended value.

 Assume depth of cutoff walls on the upstream and downstream sides = 1 m

 Here,

          ΣL_h= 4.75 m

2 ΣL_v= 2 x (2 x 1.57 + 2 x 1) = 10.28 m

H = 2 m

 Therefore,                        = 2.505

and for clay C_w = 2.3 which is less than 2.505 therefore, the structure is safe against piping. Hence the dimensions calculated are satisfactory.

References

• Das, G. (2000). Hydrology and Soil Conservation Engineering. EEE Publication. Prentice – Hall of India Pvt. Ltd. New Delhi.

• Michael, A.M., and Ojha, T.P. (2006). Principles of Agricultural Engineering. Volume-II. Jain Brothers. New Delhi.

• Murthy, V. V. N. (1985). Land and Water Management Engineering. Kalyani Publisher, New Delhi.

• Suresh, R. (1993). Soil and Water Conservation Engineering. Standard Publishers and Distributors, New Delhi.

 

Internet References

• http://www.georgiaplanning.com

• http://jps.penang.gov.my

• http://directives.sc.egov.usda.gov

• http://conservancy.umn.edu
  

Suggested Readings

• Das, G. (2000). Hydrology and Soil Conservation Engineering. EEE Publication. Prentice – Hall of India Pvt. Ltd. New Delhi.

• Michael, A.M., andOjha, T.P. (2006). Principles of Agricultural Engineering.Volume-II. Jain Brothers. New Delhi.

• Suresh, R. (1993). Soil and Water Conservation Engineering. Standard  Publishers and Distributors, New Delhi.