A canal is excavated to a depth of 4 m below ground level in a soil having C = 15 kN/m2, $ = 18°, Ysat = 20 kN/m'. The side slopes of the canal is 45°. Take Yw = 10 kN/m³. Taylor's stability number method is used to determine the factor of safety of the slope. The stability number (S) is given below. For o = 18°, Sn = 0.075 For o = 9°, Sn= 0.125 If the canal is suddenly emptied, the factor of safety of the slope is %3D

A canal is excavated to a depth of 4 m below ground level in a soil having C = 15 kN/m2, $ = 18°, Ysat = 20 kN/m'. The side slopes of the canal is 45°. Take Yw = 10 kN/m³. Taylor's stability number method is used to determine the factor of safety of the slope. The stability number (S) is given below. For o = 18°, Sn = 0.075 For o = 9°, Sn= 0.125 If the canal is suddenly emptied, the factor of safety of the slope is %3D

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Please solve a and b i need urgently. 1) A cross section of a canal is shown in Figure .The center of rotation of the sliding mass is at coordinates x = 113 m and y = 133 m. The rock surface is tangent to the slip plane. Assume the soil above the groundwater level is saturated. Use Bishop’s method. The properties of the soil are as follows along with the image. a) Determine the factor of safety for the existing condition level in the canal. b) Determine the factor of safety for a rapid drawdown of the water level in the canal.
Prob.5. A new canal is excavated to a aepth of 5 m below ground level, through a soil having the following characteristics - Cu=15 kN/m², p=15%, e = 0.78 and G = 2.72. The slope of banks is 1 in 1. Calculate the factor of safety with respect to cohesion when the canal runs full (Sn = 0.083). If it is suddenly and completely emptied (Sn = 0.122), what will be the factor of safety ?
1: An embankment is to be constructed by making use of sandy clay having the following properties: c' = 35 kN/m², o' = 25° and y= 19.5 kN/m³. The height of the embankment is 20 m with a slope of 30° with the horizontal as shown in below Figure. Estimate the factor of safety by the method of slices for the trial circle shown in the figure. 20 m 77 ww 25° A 30° 35° c'= 35 kN/m² p' = 25° y = 19.5 kN/m³ 25 m
A canal is excavated to a depth of 4 m below ground level in a soil having C = 15 kN/m², = 18°, Ysat = 20 kN/m³. The side slopes of the canal is 45°. Take Yw = 10 kN/m³. Taylor's stability number method is used to determine the factor of safety of the slope. The stability number (Sn) is given below. For = 18°, S₁ = 0.075 For 9⁰, Sn = 0.125 If the canal is suddenly emptied, the factor of safety of the slope is
A cross-section of a channel is given in Figure 3. Determine the long-term stability of the bankusing the Fellenius, and Bishop's method of slices. Note: In this type of problems, it is usually assumed that the clay above the water table(phreatic line) is fully saturated; therefore, ysat is used. R=25.6m 1c.4m Soil @ 9 3m 8-19 B k c'-197 kH/m2 13 7m 3.2 g 59tm Soile 8: 19.8kNl, c 2.67KN/ 33° BEDROCK I1.46 m to 1786m IB.6 m Figure 3
Example 23.7. A new canal is excavated to a depth of 5 m below ground level, through a soil having the following characteristics: c = 14 kN/m; = 15° e = 0.8 and G = 2.70. The slope of banks is 1 in 1. Calculate the factor of safety with respect to cohesion when the canal runs full. If it is suddenly and completely emptied, what will be the factor of safety ?
4- A moderately curved channel with a slightly rounded non-cohesive bed material with a diameter of d50 = 25 mm carrying a discharge of 30 m³/s. The longitudinal slope of the channel is 0.001 and the side wall slopes are designed to be 60% of the angle of repose of the bed material Note: Use the Strikler's formula to calculate Manning's value. Use the Swammy and Mittal's formula to estimate the critical shear stress. Use the free board depth of 0.5m. a) Design the channel using the tractive force method for a Boly ratio of 20 b) Design the channel using the most efficient hydraulic section c) Discuss about the channel stability and erosion for both designs in parts a and b Strickler (Chow, 1959) proposed a correlation between the mean diameter of bed material, dso, and the Manning's coefficient as: n = 0.039d¹/6 Swamee and Mittal (1976) proposed an explicit equation to express the Sheild's curve defined as: 50 0.409d² 1/2 (1+0.177d² )¹/¹² T = 0.155+.
A cut slope was excavated in sand. The slope is shown in following attachment . To find the properties of the sand, representative samples were taken for the soil and tested in atriaxial apparatus. A consolidated drained triaxial test was conducted. The result is given below:Chamber pressure = 103 kN/m2Deviator stress at failure = 234.6 kN/m2We know the unit weight of the sand is 16 kN/m3.Use the ordinary method of slices (use 7 slices) and estimate the factor of safety against sliding forshown slip surface and comment on the calculated factor of safety.Please note that:1. The figure is not in scale. You may resketch it in scale and calculate the factor of safety2. The slip surface is circular and passes through the toe of the embankment
4- A moderately curved channel with a slightly rounded non-cohesive bed material with a diameter of d50 = 25 mm carrying a discharge of 30 m³/s. The longitudinal slope of the channel is 0.001 and the side wall slopes are designed to be 60% of the angle of repose of the bed material Note: Use the Strikler's formula to calculate Manning's value. Use the Swammy and Mittal's formula to estimate the critical shear stress. Use the free board depth of 0.5m. a) Design the channel using the tractive force method for a Bo/y ratio of 20 b) Design the channel using the most efficient hydraulic section c) Discuss about the channel stability and erosion for both designs in parts a and b Strickler (Chow, 1959) proposed a correlation between the mean diameter of bed material, deo, and the Manning's coefficient as: n = 0.039d¹/6 Swamee and Mittal (1976) proposed an explicit equation to express the Sheild's curve defined as: T = 0.155+ To 50 0.409d² (1+0.177d²)
Hw Trapezoidal section Q = 120 m³/s S = 12 cm/km , Side slope 2:1, n= 0.0182 Compare the dimensions for two cases: 1. B/y = 4 , %3D 2. best hydraulic section
P-3 Refer to Figure, for which L, = 2.4 m, L2 = 4.6 m, y = 15.7 kN/m³, Ysat = 17.3 kN/m³, and o'=30°, and c= 35 kN/m². Assuming Sand c' = 0 C = Water table free earth support method: a. What is the theoretical depth of embedment, D? Sand Ysat c' = 0 b. What length of sheet piles is needed? c. Determine the theoretical maximum moment in the sheet pile. d. Choose a sheet pile, from next page, if the the steel pile has a oall = 172 MN/m². %3D Clay D C b'= 0
Design an irrigation channel to carry 45 m^3/Sec of discharge. The channel is to be laid at a slope of 1 in 4000. The critical velocity ratio for the soil is 1.1. Use kutter's rugorsity Coefficient as 0.025.