---
title: "Limestone attitude: square 900 m, depth at D"
subject: "Engineering Geology II"
chapter: 6
key: "semester_4/engineering_geology_ii:bh-limestone-square-900-abcd"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/bh-limestone-square-900-abcd
site: BCT Engineering
---

# Limestone attitude: square 900 m, depth at D

Engineering Geology II · Chapter 6: Measurement, analysis and interpretation of structural geological data

- Asked in: 2076 Bhadra, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/bh-limestone-square-900-abcd
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-6

## Question

A, B, C and D are four stations at the corners of a square of side 900 m on level ground. B is due west of A and C is due south of B. A limestone bed is met with in boreholes put at A, B and C at depths of 200 m, 50 m and 100 m respectively. Determine the attitude of the limestone bed. At what depth will the limestone bed occur at D?

## Short answer

Depth gradients are 0.1667 m/m east and -0.0556 m/m north. Limestone attitude is N18.4°E/10.0° ESE (dip direction 108°); at D the depth is 250 m.

## Answer

A bed is a plane, so its depth changes uniformly in plan: $d = d_A + a x + b y$, where $a$ and $b$ are the rates of change of depth per metre east and north. This is the analytical form of the three-point (strike-line) method.

#### Layout (plan, north up)
```text
   B(50) ------- A(200)      B is west of A
     |             |         C is south of B
     |             |         D is south of A
   C(100) ------ D(?)
```
Origin at A; x east, y north: A = (0, 0), B = (-900, 0), C = (-900, -900), D = (0, -900). Depths: A = 200 m, B = 50 m, C = 100 m.

#### Gradients of depth
$$
\begin{aligned}
a &= \frac{d_A - d_B}{900} = \frac{200 - 50}{900} = 0.1667\ \text{(deeper eastward)} \\
b &= \frac{d_B - d_C}{900} = \frac{50 - 100}{900} = -0.0556\ \text{(deeper southward)}
\end{aligned}
$$

#### Dip, dip direction and strike
$$
\tan\delta = \sqrt{a^2+b^2} = 0.1757 \Rightarrow \delta = 9.96^\circ
$$
The bed deepens towards the direction with east component $a = 0.1667$ and north component $b = -0.0556$, i.e. $180^\circ - \arctan(0.1667/0.0556) =$ **108.4°** (ESE). So the strike is $108.4^\circ - 90^\circ = 18.4^\circ$, i.e. **N18.4°E**.

#### Depth at D
$$
d_D = d_A + b(-900) = 200 + (-0.0556)(-900) = 250\ \text{m}
$$
Check with the parallelogram rule: $d_D = d_A + d_C - d_B = 200 + 100 - 50 = 250$ m.

**Answer: limestone attitude = N18.4°E / 10.0° towards ESE (dip direction 108°); depth at D = 250 m.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What are the depth gradients?
   A. a = 0.5
   B. a = 50/900 only
   C. a = 200/900
   D. a = 150/900 = 0.1667 and b = −50/900 = −0.0556
   Answer: D. Use A to B for x and B to C for y. (Key point: Gradients)

2. What is the depth at D?
   A. 250 m
   B. 350 m
   C. 150 m
   D. 300 m
   Answer: A. d_D = d_A + d_C − d_B = 250 m. (Key point: Depth at D)

3. What is the dip?
   A. 17.57°
   B. 9.96°, tan = sqrt(0.1667² + 0.0556²) = 0.1757
   C. 0.1757°
   D. 30°
   Answer: B. Resultant gradient. (Key point: Dip)

4. How is the strike obtained?
   A. Equal to dip direction
   B. 108.4° plus 180°
   C. Dip direction 108.4° minus 90° = N18.4°E
   D. N0°E
   Answer: C. Strike is perpendicular to dip direction. (Key point: Strike)

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