concrete cantilever retaining wall

1) A concrete cantilever retaining wall is illustrated in the accompanying figure. The objective is to assess both the sliding stability and overturning stability of the wall in accordance with the guidelines specified in AS 4678, assuming drained soil conditions.

Tasks:

(a) Determine the required base width B such that the condition
Φₙ R* = S* is satisfied for sliding stability if H = 7 m.

(b) Determine the required base width B such that the condition
Φₙ R* = S* is satisfied for overturning stability if H = 7 m.

(c) Create a plot of B versus H, where H ranges from 5 m to 9 m with a step increment of 1 m. Generate two separate plots:

• One for showing the relationship required to meet sliding stability.
• Another one for presenting the relationship required to meet overturning stability.

Note:
Assume that adequate drainage has been provided for the wall, and that the groundwater table lies well below the base of the wall, which is founded on in-situ silty clay soil.

2) A section of an anchored retaining wall is shown in the figure. The tieback anchor and soil properties are:

H = 5 m

Anchor angle = 15 degrees

Anchor depth (da) = 1.8 m

Total unit weight of sand = 20 kN/m³,

Effective friction angle = 34 degrees

Cohesion = 0 kPa

Use the Rankine’s theory of lateral pressure and apply the requirement of AS 4678.

Calculate the lateral pressures and accordingly find the minimum embedment depth of the wall (D).

Find the tension force of the anchor in kN per metre length for a safe embedded wall.

Determine the minimum free length of the anchor.

Determine the position the maximum moment of the wall.

Determine the magnitude of the maximum moment of the wall.

Note:

Assume the wall behaves as a free earth support system. The anchored wall is constructed in situ within the soil mass. The groundwater table is located well below the base of the wall, and the structure is classified as Type 2.

3) A slope is going to be excavated in a deep clayey soil deposit with two layers. The geometry of the slope is shown in the figure (not to scale). The following soil properties are given.

• Calculate the tension crack depth.
• Determine the net area of each layer and their centroid regarding the sliding circle, accounting for the depth of the crack in the given slope.
• Assume the crack is filled with water, and the water level is high, as shown in the figure. Using the information, calculate the factor of safety for the stability of slope under undrained conditions if q = 30 kPa.
• Plot the factor of safety against the surcharge load ranging from 0 to 60 kPa with an incremental step of 10 kPa.

4) Based on the definition of effective stress in unsaturated soil mechanics, calculate the effective stresses at Points A and B in a silty clay soil. Give data are as follows:
Soil suction at Point B = 40 kPa

• Air entry suction (Sae) = 30 kPa
• Unsaturated unit weight of soil = 18.8 kN/m³
• Saturated unit weight of soil = 20 kN/m³
• Assume pore air pressure = 0 kPa