Introduction:
A retaining wall is a structure that is constructed to retain soil or other materials on one side, preventing it from collapsing or sliding down. This question pertains to the design of a retaining wall that is 6m high and intended to retain dry sand. The angle of friction of the sand is 30 degrees, and the unit weight is unknown.

Calculating the Unit Weight:
The unit weight of the sand is the weight per unit volume. We can calculate this using the following formula:
Unit weight = weight/volume
We can obtain the weight of the sand by multiplying its density by its volume. The density of dry sand is around 1600 kg/m3. Therefore, the weight of the sand is:
Weight = density x volume
Volume = (6m x 6m x 6m) = 216m3
Weight = 1600 x 216 = 345,600 kg
Substituting this value in the formula above, we get:
Unit weight = 345,600 kg/216m3 = 1600 kg/m3

Determining the Lateral Earth Pressure:
The lateral earth pressure is the force acting on the retaining wall caused by the soil or sand it is retaining. We can calculate this using Rankine's theory, which assumes that the soil is cohesive and frictionless. The formula for lateral earth pressure is:
P = K x H x y
Where P is the lateral earth pressure, K is the coefficient of earth pressure, H is the height of the wall, and y is the unit weight of the soil.
For sand, the coefficient of earth pressure is given by:
K = (1 - sin φ) / (1 + sin φ)
Where φ is the angle of friction of the sand. Substituting the values given, we get:
K = (1 - sin 30) / (1 + sin 30) = 0.33
Therefore, the lateral earth pressure is:
P = 0.33 x 6m x 1600 kg/m3 = 3,840 kg/m2

Designing the Retaining Wall:
The retaining wall must be designed to withstand the lateral earth pressure calculated above. The design will depend on several factors, including the materials used, the geometry of the wall, and the stability of the foundation. Generally, retaining walls are designed with a factor of safety of 1.5 to ensure that they can withstand any additional loads that may act on them. In addition, drainage must be provided to prevent water buildup behind the wall, which can increase the lateral earth pressure and cause instability.

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