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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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,…
A cut slope was excavated in saturated clay for installation of water piping system. The
angle Bof cut slope is 45° with the horizontal. During excavation works, slope failure was
occurred when the cut reached a depth of 4.0 m. Previous soil explorations showed that a
hard layer was located at a depth of 6 m below the ground surface. The unit weight of
saturated clay is 17.5 kN/m. (Assuming an undrained condition).
1.
a)
Determine the undrained cohesion of the clay.
b)
Determine Factor of Safety (FoS) if the depth of cut slope is 3m.
c)
What is the maximum depth of saturated clay can be excavated if the Factor
of Safety (FoS) 1.4 to be implemented?
Problem 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.
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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- 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 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 soil profile is shown in Figure ?-?. Compute the shear strength on the horizontal and vertical planes at points ? and ?.arrow_forward2) In an embankment dam construction project, dam body consists of an inner clay part and outer rockflI. Which test do you prefer for the following situations, respectively: I. Before collecting water in reservoir, evaluate the short term slope stability analysis of the clay core. II. One year after collecting water in reservoir, you need to drop the water level due to an earthquake. Evaluate the slope stability of the clay core O a. Direct Shear Test-Falling Head Test O b. Direct Shear Test- Consolidated Undrained Test O . Unconsolidated Undrained Test-Consolidated Drained Tes O d. Vane Shear Test-Direct Shear Test O e. Consolidated Drained Test -Consolidated Undrained Testarrow_forwardQ.4 A 40° slope is excavated to a depth of 8 m in a deep layer of saturated clay having strength parameters c = 58 kN/m², Ø = 0, and y = 18 kN/m³. Determine the factor of safety for the trial failure surface shown in Fig. 4 Q.5 Figure 5 shows an infinite slope with H = 32 ft and the groundwater table coincidingarrow_forward
- A cut is made into a homogeneous soil as depicted in the figure below, at an angle of 60° with the horizontal. Calculate the resisting shear force in kN along the failure plane given that the shear force applied by the overlying soil wedge is 120 kN. The failure plane is at an angle of 40° from the horizontal direction and the ground water level is below this plane. Assume drained conditions for this question.arrow_forwardAn infinite slope of granular soil has a slope of 29 degrees. The soil has a dry unit weight of 18.02kN/m^3 and a saturated unit weight of 21.15kN/m^3. The soil has a depth of 5 meters over ledge rock measure vertically. Effective friction angle and soil cohesion are 14 degrees and 25 kPa, respectively. a) Compute the factor of safety considering no seepage. b) Compute the factor of safety considering full seepagearrow_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
- Please calculate the critical factor of safety for the following slope configuration using the following m ethods: Using slope stability charts Layer 1 Clay c=35 kN/sq.m Friction Angle=0 Unit Weight-18 kN/cu.m Layer 2 Silty Sand c=5 kN/sq.m Friction Angle=35 deg Unit Weight=18 kN/cu.m Slope Height=10 m Slope Angle=30 Degrees Layer 1arrow_forwardWhat is the greatest slope angle (B) of a slope formed by a cohesionless (C=0) sand? Assume the friction angle of the sand, o'= 28° O a. 280 Ob 350 OC. This sand cannot form a slope Od. Information is insufficient to determinearrow_forwardA cut slope was excavated in saturated clay for installation of water piping system. The angle Bof cut slope is 45° with the horizontal. During excavation works, slope failure was occurred when the cut reached a depth of 4.0 m. Previous soil explorations showed that a hard layer was located at a depth of 6 m below the ground surface. The unit weight of saturated clay is 17.5 kN/m³. (Assuming an undrained condition). 1. а) Determine the undrained cohesion of the clay. b) Determine Factor of Safety (FoS) if the depth of cut slope is 3m. What is the maximum depth of saturated clay can be excavated if the Factor of Safety (FoS) 1.4 to be implemented? c)arrow_forward
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