FS Route and Transportation Surveys 2 — Questions and Answers
Question 1: A parabolic vertical curve is preferred over a circular vertical curve in route surveying primarily because:
- It minimizes earthwork volumes on grades
- It provides a constant rate of change of grade (Correct answer)
- It is easier to stake in the field than a circular curve
- It provides the maximum achievable stopping sight distance
Correct answer: It provides a constant rate of change of grade
The parabola's mathematical property of constant second derivative means the grade changes at a uniform rate, making design and staking calculations straightforward.
Question 2: The prismoidal formula for computing earthwork volumes between two cross-sections is:
- V = L × (A1 + A2) / 3
- V = L × (A1 + A2) / 2
- V = L × √(A1 × A2)
- V = L × (A1 + 4Am + A2) / 6 (Correct answer)
Correct answer: V = L × (A1 + 4Am + A2) / 6
The prismoidal formula V = L(A1 + 4Am + A2)/6 uses the end areas and the area of the middle section (Am) for a more accurate volume than the average end area method.
Question 3: In earthwork terminology, 'swell' refers to:
- The rate of grade change on a vertical curve
- The increase in volume when in-situ material is excavated and loosened (Correct answer)
- The settlement of fill material under load over time
- The horizontal spreading of fill material beyond the design slope
Correct answer: The increase in volume when in-situ material is excavated and loosened
Swell is the increase in volume that occurs when compacted in-place soil is excavated and broken up, because air voids are introduced between particles.
Question 4: The K-value for a parabolic vertical curve is defined as:
- The maximum elevation difference between BVC and EVC
- The length of curve (L) divided by the algebraic difference in grades (A) (Correct answer)
- The rate of grade change per 100-foot station
- The ratio of vertical rise to horizontal distance
Correct answer: The length of curve (L) divided by the algebraic difference in grades (A)
K = L/A, where L is the curve length in feet and A is the absolute algebraic difference in grades in percent; it represents the horizontal distance needed to achieve a 1% change in grade.
Question 5: A crest vertical curve is used when:
- A positive grade is followed by a negative or less steep positive grade (Correct answer)
- A negative grade is followed by a positive or less steep negative grade
- Two grades of equal magnitude are connected
- The alignment transitions from flat terrain to a steep hill
Correct answer: A positive grade is followed by a negative or less steep positive grade
A crest (summit) vertical curve occurs when the algebraic difference in grades produces a curve that is concave downward, connecting a positive grade to a negative or flatter grade.
Question 6: In earthwork volume computations, which method provides greater accuracy when cross-section areas change significantly between stations?
- Average end area method
- Prismoidal formula (Correct answer)
- Trapezoidal approximation method
- Unit weight conversion method
Correct answer: Prismoidal formula
The prismoidal formula accounts for the intermediate cross-section and the shape of the solid more accurately than simply averaging the two end areas.
Question 7: A mass diagram in highway design is primarily used to:
- Show the elevation profile of the vertical alignment
- Determine the most economical direction and distance to haul excavated material (Correct answer)
- Calculate the total weight of earthwork material
- Plot horizontal curve locations along the alignment
Correct answer: Determine the most economical direction and distance to haul excavated material
The mass diagram graphically shows cumulative earthwork volumes and allows the designer to balance cut and fill, identify haul directions, and minimize overhaul costs.
FS Route and Transportation Surveys 2
A parabolic vertical curve is preferred over a circular vertical curve in route surveying primarily because: