ENGINEERING GEOLOGY NUMERICAL TYPE-I (a) Given Data Q1.* Ans.
VALUE ?
DIRECTION DIRECTION O
O
A limestone bed is dipping in in a dam dam site at the rate of 1 in 4 along N15 W. Find its apparent dip along N50 W. Scale 1 unit = 1cm. State Strike. O Given Data True Dip / Dip 1 in 4 N15 W O Apparent Dip ? N50 W Construction Steps 1. Draw main directions North, South, East & West. 2. Let O be the origin. O 3. Draw a line OX in direction N15 W. 4. Mark a point A on line OX at equal to 4 cm from point O. O 5. Draw a line OY in direction N50 W. 6. Draw a line, perpendicular to line OX from point A which intersects line OY at B. 7. Line AB is a strike line. 8. Measure OB. By measurement, OB is e qual to 4.9 cm. O 9. Therefore the apparent dip is 1 in 4.9 towards N50 W.
TYPE-I (b) Given Data Q2.*
True Dip / Dip Apparent Dip
True Dip / Dip Apparent Dip
VALUE VALUE
DIRECTION ?
A sandstone bed in a bridge abutment is dipping at 1 in 5 along N45OW. Find the direction in which its apparent dip is 1 in 8. State strike. Use scale 1 unit = 1 cm. O Given Data True Dip / Dip 1 in 5 N45 W Apparent Dip 1 in 8 ? Construction Steps 1. Draw main directions North, South, East & West. 2. Let O be the origin. O 3. Draw a line OX in direction N45 W. 4. Mark a point A on line OX at equal to 5 cm from point O. 5. Draw a line, perpendicular to line OX from point A. Let the line name be AC. 6. Draw an arc of 8 cm which intersect line AC at point B. 7. Line AB is strike line. 8. Line OB represents the apparent dip of magnitude 8 units. 9. Measure angle BOS. This gives the direction of the apparent dip of magnitude 8 units. O 10. The direction of apparent dip is S84 W. Note: Always there will be two apparent dip of same magnitude but different directions. Always write the direction with respect to North or South O O and the value of angle should be in between 0 - 90 .
TYPE-II Given Data
Q3.* Ans.
Apparent Dip Apparent Dip True Dip / Dip
VALUE VALUE ?
DIRECTION DIRECTION ? O
O
A sandstone bed in a mine is found to be dipping at 1:6 along S65 W and 1:8 along S15 E. Find the amount and direction of its true dip. State Strike, give the procedure. Scale 1 unit = 1 cm. O Given Data Apparent Dip 1:6 S65 W O Apparent Dip 1:8 S15 E True Dip ? ? Construction Steps 1. Draw main directions North, South, East & West. 2. Let O be the origin. O 3. Draw OA in direction S65 W and of magnitude 6 cm. O 4. Draw OB in direction S15 E and of magnitude 8 cm. 5. Join point A & B by straight line. 6. Line AB is strike line. 7. Draw line OP perpendicular to line AB from point O. 8. Line OP represents true dip. 9. Measure the length of line OP and its direction. 10. By measurement length of OP is 5.2 cm and O direction S35 W. O 11. True dip is 1:5.2 towards S35 W.
TYPE-III (Thickness of Bed) Given Data Outcrop width Inclination of bed Inclination of ground / Hill (W) (d) (s) sin( + ) Formula to ℎ, = sin( + ) ℎ, = = cos() cos() be Used Q4.* Ans.
O
O
A limestone formation is dipping at 30 East on a sloping ground of 10 West. The width of the outcrop is 160 m. Find the true and vertical thickness of limestone. Write the procedure. Scale 1 cm = 40 m. O O Given Data Outcrop width, W = 160 m Inclination of bed, d = 30 E Inclination of ground, s = 10 W = 160 × sin3 0 + 1 0 = 102.84 = 160 × sin(30 + 10)/ cos30 = 118.76 Construction Procedure 1. Draw a horizontal reference line hh’. 2. Select a point O on the reference line. O 3. From point O draw limestone bed at angle of 30 E, name the line as OA. O 4. From point O draw ground slope at angle of 10 W, name the line as OB. 5. Draw the outcrop of limestone of 4 cm (160/40) on line OB. Mark the point as C. 6. From point C draw a line CA’ parallel to line OA. 7. Draw line OX such that it perpendicular to line OA and C A’ simultaneously. This represents true thickness. 8. Draw a vertical line OY from point O, so that Y lies on line CA’. This represents vertical thickness. 9. Measure OX and OY. 10. OX=2.6 cm (2.6*40=104 m) & OY = 3.0 cm (3.0*40=120 m)
Q5.*
O
In a level ground a sandstone formation is dipping at 30 East with its outcrop 120 m wide. Find its true thickness and vertical thickness. Scale 1 cm = 40 m
Ans.
Given Data
O
Outcrop width, W = 120 m
Inclination of bed, d = 30 E
O
Inclination of ground, s = 0
= 120 × sin3 0 + 0 = 60 = 120 × sin(30 + 0)/ cos30 = 69.28 Construction Procedure 1. Draw a horizontal ground line hh’. 2. Select a point O on the ground line. O
3. From point O draw sandstone bed at angle of 30 E, name the line as OA. 4. Draw the outcrop of sandstone of 3 cm (120/40) on line hh’. Mark the point as B.
5. From point B draw a line BA’ parallel to line OA. 6. Draw line OX such that it perpendicular to line OA and BA’ simultaneously. This represents true thickness.
7. Draw a vertical line OY from point O, so that Y lies on line BA’. This represents vertical thickness.
8. Measure OX and OY. 9. OX=1.5 cm (1.5*40=60 m) & OY = 1.7 cm (1.7*40=68 m)
TYPE IV (Value of True Dip or Apparent Dip is given in Degrees) Q6.*
O
O
O
O
The apparent dip of shale bed is 30 in a direction of S30 E and 45 in a direction of S58 W. Find the direction and amount of its true dip. Scale 1 cm = 1 unit. Given Data
O
S30 E
45
O
S58 W
?
?
Apparent Dip
30
Apparent Dip True Dip
O
O
Construction procedure 1. Draw main directions North, South, East & West. 2. Let O be the origin. O
3. Draw OX at an angle of S30 E. 4. Draw OC at right angle with OX and measure OC equal to 1 unit. O
5. Similarly draw OY at an angle of S58 W and draw OD at right angle to OY of length 1 unit. O
O
O
6. From point C, draw a line at angle 60 (i.e. 90 – 30 ), which meets line OX at point A. O
O
O
7. From point D, draw a line at angle of 45 (i.e. 90 – 45 ), which meets line OY at point B. 8. Join points A & B by straight line. 9. AB represents strike line. 10. Draw a perpendicular line from point O to line AB. Name line the line as OE. 11. Draw OF at right angle with OE and measure OF equal to 1 unit. 12. Join points E & F by straight line. O
13. Angle OEF represents the true dip of shale bed. By measurement we find the true dip of bed as 49 towards O
S30 W.
Q7.* Ans.
O
O
In a dam site, a sandstone bed is found to be dipping at 35 along S40 W. Find the direction in which apparent O dip is 22 . State strike and give procedure. O O Given Data True Dip / Dip 35 S40 W O Apparent Dip 22 ? Construction Procedure 1. Draw main directions North, South, East & West. 2. Let O be the origin. O 3. Draw OX at an angle of S40 W. 4. Draw OC at right angle with OX and measure OC equal to 1 unit. O O 14. From point C, draw a line at angle 55 (i.e. 90 – O 35 ), which meets line OX at point A. 15. Similarly draw OY at any angle and draw OD at right angle to OY of length 1 unit. O O 16. From point D, draw a line at angle of 68 (i.e. 90 – O 22 ), which meets line OY at point Z. 17. Draw a arc with center O and radius OZ. The arc represents various apparent dip loci which are possible. 18. From point A draw line perpendicular to line OX, which intersect the arc at point B. 19. Line AB represents strike line. 20. Join the points O & B by straight line. 21. Angle SOB represents the direction of apparent dip. 22. By measuring the direction of apparent dip is O See the note of Question no 02 S14 E.
TYPE-V (Three point problem) Q8. Ans.
On dipping sandstone the A (400, 1200, 3400), B (1000, 200, 2700), and C (2200, 900, 2400) are three points on the surface of rock whose x, y and z coordinates are given. Determine the slope of sandstone. Construction Steps 1. Draw x-axis and y-axis to scale of 1:200. 8. Draw a line AF parallel to line DE where point F lies 2. Plot the points A, B, C as per their x & y on line ff’. coordinates. 9. Let us assume the elevation of ff’ line 3400. 3. The z coordinates of B (2700) lies in between A 10. Draw lines parallel to ff’ at an elevation of 2700 (3400) & C (2400). Therefore a contour line passing (gg’) & 2400 (hh’). The distance between ff’ & gg’ is through B must cross the line segment AC 3.5 units and ff’ & hh’ is 5 units. 1 4. Mark a point D on line AC such that point D will 3400 − 2700 ∗ = 3.5 have the elevation of 2700 and it divides the line 200 1 AC in ratio of 7:3. 3400 − 2400 ∗ = 5.0 3400 − 2700 7 200 = = 11. Extend the DE till point G which lies on line gg’ 2700 − 2400 3 5. Join point B & D. Line BD represents strike line 12. Draw a line CH parallel to line DE, H point lies on line hh’. having elevation 2700. 6. Extend the line BD on downward side by distance 13. Measure the angle EFH, it gives the true dip of sandstone. as per your convenience. Name the last point on O 14. By measuring the value is coming 32 . So the true line BD as E. O dip of sandstone is 32 . 7. From point E draw a perpendicular line ff’.
Notes
Always draw figures and write construction steps (if it is not mentioned then also write steps and draw figure)
Always mentioned the strike line in construction steps. Do not forget to write scale on top-right corner of map.
Write the final answer in the drawing as well as in construction steps.
