Principles of Geotechnical Engineering (MindTap Course List)
9th Edition
ISBN: 9781305970939
Author: Braja M. Das, Khaled Sobhan
Publisher: Cengage Learning
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Chapter 15, Problem 15.14P
To determine
Find the height (H) of the slope if the factor of safety is 2.5.
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CENTER OF
FAILURE CIRCLE
soil 1
unit weight = 16 kN/m3
c = 20 kPa
' = 25 deg
soil 2
unit weight = 18 kN/m3
c = 30 kPa
= 35 deg
Scale 1 cm = 2m
Figure shows an embankment consisting of two soils
with the given soil properties. There is no ground
water table in the vicinity.
(a) Calculate the factor of safety using the Ordinary
Method of Slices
(b) Assuming a factor of safety of 1.5, perform one
iteration to calculate factor of safety using the
Bishop?s Method of Slices
Geotechnical engineering
You are required to analyse a slope stability problem using the Swedish method for failure along the slip surface as shown in the figure below. The slope is inclined at an angle of 30° to the horizontal and has a height of 10 m. The ground water table (GWT) is located at a depth of 5.1 m below the crest. It goes along the slope and reaches at the toe level as shown in the figure.
Soil investigation revealed that the site consists of a layer of silty clay overlying a layer of sand. Assume c = (40 + 2x) kPa and ϕ = 10° for the silty clay, and c = 0 and ϕ = (30 + x)° for the sand layer; where x is the last digit of your student ID (e.g., if your student ID is 5746189, x = 9). All slices have equal width (b = 2.89 m) and the slices are numbered 1‒6 from left to right. The coordinates of the midpoint of the bases (M , M , M , M , M , M ) of the slices are shown on the right side of the figure. The weights of slices 1‒6 are as follows (in kN/m): W1 = 53.5, W2 = 141.3, W3 = 199.6, W4= 224.8,…
Chapter 15 Solutions
Principles of Geotechnical Engineering (MindTap Course List)
Ch. 15 - Prob. 15.1PCh. 15 - Prob. 15.2PCh. 15 - Prob. 15.3PCh. 15 - Prob. 15.4PCh. 15 - Prob. 15.5PCh. 15 - Prob. 15.6PCh. 15 - Prob. 15.7PCh. 15 - Prob. 15.8PCh. 15 - Prob. 15.9PCh. 15 - Prob. 15.10P
Ch. 15 - Prob. 15.11PCh. 15 - Prob. 15.12PCh. 15 - Prob. 15.13PCh. 15 - Prob. 15.14PCh. 15 - Prob. 15.15PCh. 15 - Prob. 15.16PCh. 15 - Prob. 15.17PCh. 15 - Prob. 15.18PCh. 15 - Prob. 15.19PCh. 15 - Prob. 15.20PCh. 15 - Prob. 15.21PCh. 15 - Prob. 15.22PCh. 15 - Prob. 15.23PCh. 15 - Prob. 15.27PCh. 15 - Prob. 15.28PCh. 15 - Prob. 15.29PCh. 15 - Prob. 15.30PCh. 15 - Prob. 15.31PCh. 15 - Prob. 15.32P
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- Please answer 15.15arrow_forwardCompute the angle of internal friction. The results of a three consolidated undrained tri-axial test on saturated clay are as follows: a. 15.03°b. 12.06°c. 18.40°d. 31.05°arrow_forwardA 9m cut slope is shown in the figure. The unit weight of soil is 17kN/m3. Friction angle and cohesion along the rock surface are 20 degrees and 24kPa respectively. The slope makes an angle of 300 from horizontal and the failure plane is at 150. Determine the developed frictional force on the failure plane.arrow_forward
- A 30° slope has a height of 10 m as shown in the figure below. The soil in the slope has the following parameters c = 20 kPa, ϕ = 0°, γ = 18 kN/m . Calculate the factor of safety for the slip surface shown in the figure.arrow_forwardThe results of a three consolidated undrained tri-axial test on saturated clay are as follows: Compute the angle of internal friction a. 15.03 degreesb. 12.06 degreesc. 18.40 degreesd. 31.05 degreesarrow_forwardThe excavation shown below will be made on the clay for the construction of a highway. Potential Slope stability analysis is required on the slip plane. The ground is silty clay and c '= 18 kPa,' '= 20o and water = 100 kPa. At point a If the shear stress is 60 kPa, calculate the safety coefficient for this point.arrow_forward
- b=1,5arrow_forwardProblem 1Explain whether the following are true or false. 1. A lower safety factor implies that a greater fraction of the shear strength is mobilized along the failure surface. 2. In an undrained slope of 1.0 (horizontal): 1.5 (vertical), the critical circle is always a toe circle. 3. The mid-point circle passes through the toe. 4. Taylor’s stability charts can be used only for homogeneous soils.arrow_forwardA vertical cut has been made into a homogeneous soil as depicted in the figure. What should the depth of the cut (H) be in metres so that the factor of safety for the failure plane shown is equal to 1.5? The failure plane is at an angle of 30° from the horizontal direction and the ground water level is below this plane. Assume undrained conditions for this question.arrow_forward
- The figure below shows a proposed site where an excavation will be made. The 12 ft layer of sand will be removed, so that the top of the 30 ft normally consolidated clay layer will be exposed (Assume that changes in GWT do not affect γt of clay). a. Assume that the water-table location remains the same during excavation. Compute the σ, σ′v, and u values at the middle of the clay layer before and after the excavation b. Assuming 1-D conditions, compute how much the clay layer will deform due to this excavation, in inches. Specify whether this is settlement or heavearrow_forwardA compacted fill slope is to be made of a soil with a c' = 200 lb/ft?, p'= 30° and y= 122 Ib/ft. Using an infinite slope analysis and assuming a failure surface 4.0 ft vertically below the ground surface and a groundwater table 1.3 ft below the ground surface, determine the steepest allowable slope ratio that will maintain a factor of safety at least 1.5. This analysis considers only surficial stability and a separate analysis would need to be conducted to evaluate the potential for a deep-seated slide in the fill. Hint: This may involve iteration using a spreadsheet or a similar approach.arrow_forwardA cut slope in soft clay has been constructed as part of a road alignment. The slope is 21.8 degrees and 10 m high. The unit weight of the soft clay is 18kN/m3. (i) A walk over survey recently indicated signs of instability. Samples have been collected from the slope and the drained analysis parameters for the soil have been determined as follows: Soil properties: φ'= 24 º, c'=2.5kPa, γd=19kN/m3 , γsat=20kN/m3 Based on the effective stress parameters given, perform a quick initial estimate of the factor of safety of this slope using Bishop and Morgernsterns charts. Assume an average pore water pressure ratio (ru) of 0.3 for the slopearrow_forward
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