Soil placed in a dense state is compacted to increase shear strength, decrease future settlement, decrease permeability, and increase the stability of slopes and embankments.
The moisture content at which the maximum dry unit weight is attained is called the optimum moisture content. The laboratory test used to obtain maximum dry unit weight and optimum moisture content is the Proctor compaction test.
Use $w$ as a decimal in computations. If water content is given in percent, divide by 100 before substituting.
The zero-air-void unit weight assumes all void spaces are filled with water, so $S=100\%$.
Common field unit weight methods are the sand cone method, rubber balloon method, and nuclear method.
A soil has $G_s=2.70$, $e_{max}=0.75$, $e_{min}=0.46$, $D_r=76\%$, and water content of 8 percent. Compute the moist unit weight of compaction in the field.
Answer: 18.70 kN/m3.
A uniform sand has porosity of 43 percent. Its void ratio in the loosest condition is 0.85 and in the densest condition is 0.35. Determine the density index.
Answer: 19.1 percent.
The field density is 1960 kg/m3, particle density is 2700 kg/m3, $e_{max}=0.69$, $e_{min}=0.44$, and water content is 11 percent. Compute the relative density.
Answer: 64.4 percent.
A field sample has mass 1830 g and volume 0.001 m3. If $G_s=2.60$, water content is 10 percent, $e_{max}=0.62$, and $e_{min}=0.43$, compute the relative density.
Answer: 30.1 percent.
A laboratory compaction test gives a maximum dry density of 1486 kg/m3. The in situ water content is 17.46 percent and the field density is 1660 kg/m3. Compute the relative compaction.
Answer: 95.1 percent.
The maximum and minimum dry unit weights of sand are 18.31 kN/m3 and 15.25 kN/m3. Determine field dry unit weight if relative density is 64 percent.
Answer: 17.08 kN/m3.
A silty sand has $e_{max}=0.86$, $e_{min}=0.30$, $D_r=54\%$, and dry unit weight of 16.85 kN/m3. Compute the specific gravity.
Answer: $G_s = 2.68$.
For sandy soil, $e_{max}=0.75$, $e_{min}=0.46$, $G_s=2.68$, $D_r=78\%$, and water content is 9 percent. Determine in situ void ratio, moist unit weight, and dry unit weight.
Answer: $e=0.524$, $\gamma=18.81$ kN/m3, and $\gamma_d=17.25$ kN/m3.
8000 m3 of soil is excavated with $e=1.20$, $G_s=2.67$, borrow water content of 15 percent, and required in-place water content of 18 percent. How much water must be added in cubic meters?
Answer: About 291 m3 of water.
Relative compaction is 93.5 percent. Maximum and minimum dry unit weights are 16.98 kN/m3 and 14.46 kN/m3. Determine field dry unit weight.
Answer: 15.88 kN/m3.
Relative compaction is 95 percent, maximum dry unit weight is 16 kN/m3, and moisture content is 8 percent. Compute the moist unit weight.
Answer: 16.42 kN/m3.
A borrow soil has natural water content of 10 percent and bulk density of 1800 kg/m3. It is used for an embankment compacted to a dry density of 1850 kg/m3. How many cubic meters of excavation are required for 1 m3 of compacted embankment?
Answer: 1.13 m3 of excavation per 1 m3 compacted embankment.
The maximum and minimum dry unit weights are 18.31 kN/m3 and 15.25 kN/m3. What is the relative compaction if relative density is 64 percent?
Answer: 93.3 percent.
Relative compaction is 94 percent, $\gamma_{d,max}=16.2$ kN/m3, $\gamma_{d,min}=14.9$ kN/m3, and water content is 8 percent. Determine field moist unit weight.
Answer: 16.45 kN/m3.
Moist soil removed from a test hole weighs 10.18 N. Oven-dry weight is 8.97 N. Test-hole volume is 0.000479 m3. Laboratory maximum dry unit weight is 19.34 kN/m3. Determine percent compaction.
Answer: 96.8 percent.
From a compaction curve, the maximum dry unit weight is 19.6 kN/m3 and optimum moisture content is 11.3 percent. If $G_s=2.70$, compute the degree of saturation at optimum moisture content.
Answer: Maximum dry unit weight = 19.6 kN/m3, OMC = 11.3 percent, and $S=86.8\%$.
A sand cone test gives hole volume = 0.0014 m3, moist soil mass = 3 kg, water content = 12 percent, and laboratory maximum dry unit weight = 19 kN/m3. Determine field relative compaction.
Answer: 98.8 percent.
A borrow pit soil has void ratio 1.15. It will be compacted to fill 100,000 m3 with final void ratio 0.73. Determine the borrow volume required, assuming the volume of solids is conserved.
Answer: About 124,300 m3.
A sand cone test gives initial apparatus mass = 5.912 kg, final apparatus mass = 2.378 kg, soil recovered = 2.883 kg, moisture content = 7 percent, sand density = 1300 kg/m3, cone volume = $1.114 \times 10^{-3}$ m3, and maximum dry unit weight = 19 kN/m3. Compute moist unit weight, dry unit weight, and relative compaction.
Answer: $\gamma=17.63$ kN/m3, $\gamma_d=16.47$ kN/m3, and $R=86.7\%$.
Increasing compaction energy shifts the compaction curve upward and to the left. This means higher maximum dry unit weight is achieved at a lower optimum moisture content. The standard Proctor test uses 600 kN·m/m3 of energy, while the modified Proctor test uses about 2700 kN·m/m3. The modified Proctor yields roughly 5 percent higher dry unit weight and 2 to 3 percent lower optimum moisture content compared to the standard test.
The zero air voids line does not shift with compaction energy because it depends only on specific gravity and water content. All compaction curves for a given soil must fall to the left of the zero air voids line.
A standard Proctor mold has a volume of 943.3 cm3. After compaction, the moist soil mass in the mold is 1845 g. A moisture content test on the same soil gives a wet mass of 52.3 g and a dry mass of 46.1 g. Compute the moist unit weight and the dry unit weight.
Answer: $\gamma=19.18$ kN/m3 and $\gamma_d=16.91$ kN/m3.
A compacted soil has $G_s = 2.72$, a dry unit weight of 18.0 kN/m3, and a water content of 10 percent. Compute the void ratio, degree of saturation, and percentage of air voids $V_a/V$.
Answer: $e=0.483$, $S=56.3\%$, and air voids $=14.3\%$.
A contractor is preparing a soil embankment. The borrow soil has $G_s=2.68$, dry unit weight of 14.8 kN/m3, and natural water content of 8 percent. The required conditions are a dry unit weight of 17.2 kN/m3 and water content of 14 percent. Per cubic meter of compacted fill, how many kilograms of water must be added to the borrow material before compaction?
Find the volume of borrow material required per 1 m3 of compacted fill by conserving the mass of solids:
Answer: About 105.2 kg of water must be added per cubic meter of compacted fill.
A roadway embankment requires 50,000 m3 of compacted fill with a void ratio of 0.65. The borrow pit soil has a void ratio of 1.10 and the in-situ soil at cut sections has a void ratio of 0.80. Determine the volume of material to excavate from the cut section to produce the required fill, assuming the mass of solids is conserved.
Alternatively, from borrow pit:
Answer: About 54,545 m3 must be cut from the in-situ section (or 63,636 m3 from the borrow pit with its higher void ratio).