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The accompanying map, located on the back page of Section A, shows ground contours at five metre vertical intervals - Leaving Cert DCG - Question C-1 - 2018
Question C-1
The accompanying map, located on the back page of Section A, shows ground contours at five metre vertical intervals. AD is the centreline of a proposed motorway. The... show full transcript
Worked Solution & Example Answer:The accompanying map, located on the back page of Section A, shows ground contours at five metre vertical intervals - Leaving Cert DCG - Question C-1 - 2018
Step 1
Using side slopes of 1 in 1.5 for the cuttings and 1 in 2 for the embankments, complete the earthworks necessary to accommodate the motorway between A and D on the northern side.
Answer
To determine the earthworks for the motorway between A and D:
- Identify the Altitudes: The altitude of A and B is 65m. From B to C, the elevation remains 65m, and from C to D, the stratum rises at a gradient of 1 in 15. Hence, we can calculate the altitude of D.
- Calculate the Elevation of D: If the horizontal distance from C to D is 'x', the altitude can be calculated: ext{Elevation of D} = 65 + rac{x}{15}
- Cutting and Embankment Dimensions: Utilize side slopes of 1 in 1.5 for cuttings and 1 in 2 for embankments to calculate the earthworks volume.
- For a width 'w' of the motorway at level elevation:
- Cutting dimensions: Depth = Elevation difference, Width = Cutting slope dimensions.
- Embankment dimensions: Height = Difference from existing land to motorway requirements, Width based on slope gradients.
- For a width 'w' of the motorway at level elevation:
- Draw Your Final Output: Summarize calculations in a diagram representing the cuts and fills necessary, ensuring to label topography and incline gradients clearly.
Step 2
(i) In the space provided at the top of the page, draw the elevation of the triangular portion of the top surface of the stratum.
Answer
- Identify the points: Based on the altitude, plot points P (45m), Q (60m), and R (35m) on a graph, ensuring accurate representation of their heights.
- Draw the Elevation Triangle: Connect points P, Q, and R to form the triangular elevation, ensuring angles reflect the geographical changes respective to each point.
Step 3
(ii) Draw in the plan of the triangle and determine the strike and dip of the stratum.
Answer
- Create a horizontal projection: On a separate plan view, mark points P, Q, and R's horizontal positions.
- Draw the triangle: Connect the points to form the base of your triangle.
- Determine Strike: Measure the angle of the line between any two points, use trigonometric functions to compute the strike.
- Calculate Dip: Use the elevation differences between points to determine the dip angle using the formula:
ext{Dip} = an^{-1}igg( rac{ ext{Altitude difference}}{ ext{Horizontal distance between points}}igg).
Step 4
(iii) Determine, and indicate in metres, the length of the shortest skew borehole from R to the top surface of the stratum.
Answer
- Measure from point R: Identify R's coordinates on the plan view and the elevation line determined earlier.
- Use the three-dimensional distance formula: Calculate the skew distance from R (at 35m elevation) to the elevation of the triangle at R: d = rac{ ext{Vertical change}^2 + ext{Horizontal change}^2}{ ext{H}}
- Include elevation data: Ensure calculations take into account the topography of the triangular elevation, indicating how deep the borehole must reach vertically.
Step 5
Determine, in plan, the line of intersection between the top surface of the stratum and the surface of the widened portion of the toll plaza.
Answer
- Assess the top elevation and toll plaza width: Identify the altitudes of areas in question and sections that are widened.
- Determine intersection points: Use the previously calculated elevation points to sketch in the line where the top of the stratum meets the toll plaza widening, identifying any slopes or dips present in the surface.
- Final Fusion of Data: Clearly annotate this on the plan, recognizing any geographical constraints or features affecting the intersection.