## PEC EPE Engineering Geology Numerical Questions

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### Other PEC EPE Exam Past Paper Questions

Calculate the volume of a sedimentary rock layer with a length of 20 meters, width of 10 meters, and thickness of 2 meters.

Solution:

Volume = Length ร Width ร Thickness

Volume = 20 m ร 10 m ร 2 m = 400 cubic meters

Answer: Volume of the sedimentary rock layer = 400 cubic meters

A sample of soil has a porosity of 40%. Calculate the volume of void spaces in a 10 cubic meter soil sample.

Solution:

Volume of void spaces = Porosity ร Total volume

Volume of void spaces = 0.40 ร 10 cubic meters = 4 cubic meters

Answer: Volume of void spaces in the soil sample = 4 cubic meters

Calculate the weight of a rock sample with a density of 2,500 kg/mยณ and a volume of 5 cubic meters.

Solution:

Weight = Density ร Volume

Weight = 2,500 kg/mยณ ร 5 cubic meters = 12,500 kg

Answer: Weight of the rock sample = 12,500 kg

A geological survey team measures the strike of a rock layer to be 30 degrees and the dip to be 20 degrees. Calculate the true dip of the rock layer.

Solution:

True dip = Dip / Cos(Strike)

True dip = 20 degrees / Cos(30 degrees) โ 23.09 degrees

Answer: True dip of the rock layer โ 23.09 degrees

A rock sample weighs 500 N in air and 300 N when fully submerged in water. Calculate the specific gravity of the rock.

Solution:

Specific Gravity = Weight in air / (Weight in air – Weight in water)

Specific Gravity = 500 N / (500 N – 300 N) = 500 N / 200 N = 2.5

Answer: Specific Gravity of the rock โ 2.5

The water content of a soil sample is 15%. Calculate the dry unit weight of the soil if its saturated unit weight is 18 kN/mยณ.

Solution:

Dry unit weight = Saturated unit weight ร (1 – Water content)

Dry unit weight = 18 kN/mยณ ร (1 – 0.15) = 18 kN/mยณ ร 0.85 โ 15.3 kN/mยณ

Answer: Dry unit weight of the soil โ 15.3 kN/mยณ

Calculate the void ratio of a soil sample if its porosity is 35%.

Solution:

Void ratio = Porosity / (1 – Porosity)

Void ratio = 0.35 / (1 – 0.35) = 0.35 / 0.65 โ 0.5385

Answer: Void ratio of the soil sample โ 0.5385

A soil sample has a total volume of 20 cubic meters and a void ratio of 0.6. Calculate the volume of void spaces in the sample.

Solution:

Volume of void spaces = Void ratio ร Total volume

Volume of void spaces = 0.6 ร 20 cubic meters = 12 cubic meters

Answer: Volume of void spaces in the soil sample โ 12 cubic meters

A geological formation is composed of limestone (density = 2,700 kg/mยณ) overlain by shale (density = 2,000 kg/mยณ). Calculate the average density of the formation if the thickness of limestone is 15 meters and the thickness of shale is 10 meters.

Solution:

Average density = (Density of limestone ร Thickness of limestone + Density of shale ร Thickness of shale) / (Total thickness)

Average density = (2,700 kg/mยณ ร 15 m + 2,000 kg/mยณ ร 10 m) / (15 m + 10 m) โ 2,333.33 kg/mยณ

Answer: Average density of the geological formation โ 2,333.33 kg/mยณ

The porosity of a soil sample is 20% and its dry unit weight is 16 kN/mยณ. Calculate its saturated unit weight if the water content is 12%.

Solution:

Saturated unit weight = Dry unit weight / (1 – Water content)

Saturated unit weight = 16 kN/mยณ / (1 – 0.12) = 16 kN/mยณ / 0.88 โ 18.18 kN/mยณ

Answer: Saturated unit weight of the soil โ 18.18 kN/mยณ

A rock sample weighs 600 N in air and 500 N when fully submerged in water. Calculate the apparent specific gravity of the rock.

Solution:

Apparent Specific Gravity = Weight in air / (Weight in air – Buoyant force)

Buoyant force = Weight in air – Weight in water

Buoyant force = 600 N – 500 N = 100 N

Apparent Specific Gravity = 600 N / (600 N – 100 N) = 600 N / 500 N = 1.2

Answer: Apparent Specific Gravity of the rock = 1.2

A soil sample has a total volume of 15 cubic meters and a void ratio of 0.7. Calculate the volume of solids in the sample.

Solution:

Volume of solids = Total volume / (1 + Void ratio)

Volume of solids = 15 cubic meters / (1 + 0.7) = 15 cubic meters / 1.7 โ 8.82 cubic meters

Answer: Volume of solids in the soil sample โ 8.82 cubic meters

Calculate the weight of a rock sample with a density of 2,400 kg/mยณ and a volume of 4 cubic meters.

Solution:

Weight = Density ร Volume

Weight = 2,400 kg/mยณ ร 4 cubic meters = 9,600 kg

Answer: Weight of the rock sample = 9,600 kg

A geological survey team measures the strike of a rock layer to be 45 degrees and the dip to be 30 degrees. Calculate the true dip of the rock layer.

Solution:

True dip = Dip / Cos(Strike)

True dip = 30 degrees / Cos(45 degrees) โ 42.43 degrees

Answer: True dip of the rock layer โ 42.43 degrees

A rock sample weighs 800 N in air and 700 N when fully submerged in water. Calculate the specific gravity of the rock.

Solution:

Specific Gravity = Weight in air / (Weight in air – Buoyant force)

Buoyant force = Weight in air – Weight in water

Buoyant force = 800 N – 700 N = 100 N

Specific Gravity = 800 N / (800 N – 100 N) = 800 N / 700 N โ 1.14

Answer: Specific Gravity of the rock โ 1.14

The water content of a soil sample is 20%. Calculate the dry unit weight of the soil if its saturated unit weight is 20 kN/mยณ.

Solution:

Dry unit weight = Saturated unit weight ร (1 – Water content)

Dry unit weight = 20 kN/mยณ ร (1 – 0.20) = 20 kN/mยณ ร 0.80 = 16 kN/mยณ

Answer: Dry unit weight of the soil โ 16 kN/mยณ

Calculate the void ratio of a soil sample if its porosity is 25%.

Solution:

Void ratio = Porosity / (1 – Porosity)

Void ratio = 0.25 / (1 – 0.25) = 0.25 / 0.75 โ 0.3333

Answer: Void ratio of the soil sample โ 0.3333

A soil sample has a total volume of 25 cubic meters and a void ratio of 0.5. Calculate the volume of void spaces in the sample.

Solution:

Volume of void spaces = Void ratio ร Total volume

Volume of void spaces = 0.5 ร 25 cubic meters = 12.5 cubic meters

Answer: Volume of void spaces in the soil sample โ 12.5 cubic meters

A geological formation is composed of sandstone (density = 2,200 kg/mยณ) overlain by shale (density = 2,100 kg/mยณ). Calculate the average density of the formation if the thickness of sandstone is 12 meters and the thickness of shale is 8 meters.

Solution:

Average density = (Density of sandstone ร Thickness of sandstone + Density of shale ร Thickness of shale) / (Total thickness)

Average density = (2,200 kg/mยณ ร 12 m + 2,100 kg/mยณ ร 8 m) / (12 m + 8 m) โ 2,160 kg/mยณ

Answer: Average density of the geological formation โ 2,160 kg/mยณ

The porosity of a soil sample is 30% and its dry unit weight is 18 kN/mยณ. Calculate its saturated unit weight if the water content is 10%.

Solution:

Saturated unit weight = Dry unit weight / (1 – Water content)

Saturated unit weight = 18 kN/mยณ / (1 – 0.10) = 18 kN/mยณ / 0.90 โ 20 kN/mยณ

Answer: Saturated unit weight of the soil โ 20 kN/mยณ