---
title: "Limestone true thickness across stream"
subject: "Engineering Geology II"
chapter: 6
key: "semester_4/engineering_geology_ii:stream-limestone-true-thickness"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/stream-limestone-true-thickness
site: BCT Engineering
---

# Limestone true thickness across stream

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

- Asked in: 2069 Poush, 5 marks
- Video: [Help video for calculating true thickness](https://www.youtube.com/watch?v=bJSBg7VTzM4) — Catherine Mottram
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/stream-limestone-true-thickness
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-6

## Question

A stream flows in a southerly direction across a limestone that strikes N30°W and dips 50°SW. Determine the true thickness of the limestone if the base of the limestone is exposed at an altitude of 2900 m and the top is exposed at an altitude of 2000 m. The breadth of the limestone along the stream is 2100 m.

## Short answer

True thickness for sloping ground: t = w sinθ sinδ – h cosδ. With breadth w=2100 m, strike N30°W, dip 50°SW, stream south, height drop h=900 m, θ=30°, t = 2100 sin30° sin50° – 900 cos50° = 225.8 m.

## Answer

**Principle:** the true thickness is the perpendicular distance between the top and bottom surfaces of the bed. When the traverse is on sloping ground it is computed from the horizontal distance along the traverse and the difference in height.

#### Given
Strike N30°W (330°), dip 50° SW (dip direction 240°). Stream flows south (180°). Horizontal distance (breadth) along the stream $w = 2100$ m. Base is at 2900 m and top at 2000 m, so the height difference $h = 900$ m (the ground falls from base to top, i.e. downstream, which is in the dip direction).

#### Step 1: angle between traverse and strike
Strike line 330° (or 150°); traverse bearing 180°: $\theta = 180^\circ - 150^\circ = 30^\circ$.

#### Step 2: thickness for level ground
$$
t_0 = w\sin\theta\sin\delta = 2100\sin 30^\circ\sin 50^\circ = 804.35\ \text{m}
$$

#### Step 3: correction for slope of ground
The ground falls in the direction of dip, so the height difference reduces the thickness:
$$
\begin{aligned}
t &= w\sin\theta\sin\delta - h\cos\delta \\
&= 804.35 - 900\cos 50^\circ \\
&= 804.35 - 578.51 = 225.84\ \text{m}
\end{aligned}
$$

**Answer: true thickness of the limestone = 225.8 m (about 226 m).**

## Check yourself

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

1. The stream flows south and strike is N30°W. What is the angle θ between traverse and strike?
   A. 60°
   B. 30°
   C. 50°
   D. 90°
   Answer: B. Strike line bearing 150° and traverse 180° differ by 30°. (Key point: Angle to strike)

2. What is the thickness formula for level ground?
   A. t0 = w cos θ cos δ
   B. t0 = w sin θ cos δ
   C. t0 = w / (sin θ sin δ)
   D. t0 = w sin θ sin δ
   Answer: D. Perpendicular width across strike is w sin θ, and its component normal to the bed is times sin δ: 804.35 m here. (Key point: Level-ground thickness)

3. Why is h cos δ subtracted?
   A. The ground rises against the dip, so it must be added
   B. The ground falls in the dip direction, so the height difference reduces the thickness
   C. Because stream erosion removed part of the bed
   D. Because the dip is steeper than the ground
   Answer: B. When the slope is in the dip direction, t = w sin θ sin δ - h cos δ. (Key point: Slope correction)

4. What true thickness is obtained?
   A. About 804.4 m
   B. About 1383 m
   C. About 578.5 m
   D. About 225.8 m
   Answer: D. 804.35 - 900 cos 50° = 804.35 - 578.51 = 225.84 m. (Key point: Result)

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