---
title: "Drained and CU tests on two samples"
subject: "Soil Mechanics"
chapter: 10
key: "semester_4/soil_mechanics:drained-and-cu-two-samples-parameters"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/drained-and-cu-two-samples-parameters
site: BCT Engineering
---

# Drained and CU tests on two samples

Soil Mechanics · Chapter 10: Shear Strength of Soil

- Asked in: 2079 Jestha, 6 marks
- Video: [Shear Strength of Soils Examples (Q5 - Consolidated-Undrained triaxial test) - Soil Mechanics I](https://www.youtube.com/watch?v=7nFA-VIP4GQ) — Civil Engineering with Amir
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/drained-and-cu-two-samples-parameters
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-10

## Question

The results of drained and consolidated-undrained triaxial tests on two samples of normally consolidated clay are shown below.

| Type of test | $\sigma_3$ (kPa) | $\sigma_1 - \sigma_3$ at peak (kPa) |
|---|---|---|
| Drained | 300 | 650 |
| Consolidated-undrained | 200 | 250 |

Determine: (i) $\phi'$ from the drained test, (ii) $\phi$ from the consolidated-undrained test, (iii) the pore pressure in the consolidated-undrained test at failure.

## Short answer

Drained test: φ′ = arcsin(650/(300+950)) = 31.3°. CU test: φcu = arcsin(250/(200+450)) = 22.6°. Pore pressure at failure: using φ′=31.3°, σ3′ = 115.4 kPa, so uf = 200−115.4 = 84.6 kPa.

## Answer

For normally consolidated clay, $c' = 0$ and $c_{cu} = 0$, so $\sin\phi = \dfrac{\sigma_1-\sigma_3}{\sigma_1+\sigma_3}$.

#### (i) $\phi'$ from the drained test

$\sigma_3' = 300$, $\sigma_1' = 300+650 = 950$ kPa.

$$
\sin\phi' = \frac{650}{300+950} = \frac{650}{1250} = 0.52 \;\Rightarrow\; \phi' = 31.3^\circ
$$

#### (ii) $\phi$ from the CU test (total stress)

$\sigma_3 = 200$, $\sigma_1 = 200+250 = 450$ kPa.

$$
\sin\phi_{cu} = \frac{250}{200+450} = \frac{250}{650} = 0.385 \;\Rightarrow\; \phi_{cu} = 22.6^\circ
$$

#### (iii) Pore pressure at failure in the CU test

Assume the same effective friction angle holds, $\phi' = 31.3^\circ$, and $c'=0$. At failure the effective Mohr circle has the same deviator stress, 250 kPa:

$$
\sin\phi' = \frac{\sigma_1'-\sigma_3'}{\sigma_1'+\sigma_3'} = \frac{250}{2\sigma_3' + 250} = 0.52
$$

$$
2\sigma_3' + 250 = \frac{250}{0.52} = 480.8 \;\Rightarrow\; \sigma_3' = 115.4\ \text{kPa}
$$

$$
u_f = \sigma_3 - \sigma_3' = 200 - 115.4 = 84.6\ \text{kPa}
$$

**Answer: (i) $\phi' = 31.3^\circ$; (ii) $\phi_{cu} = 22.6^\circ$; (iii) $u_f \approx 84.6$ kPa.**

## Check yourself

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

1. Why can sin phi = (sigma_1 - sigma_3)/(sigma_1 + sigma_3) be used?
   A. For normally consolidated clay c' = 0 and c_cu = 0, so the envelope passes through the origin
   B. Because pore pressure is always zero
   C. Because the clay is overconsolidated
   D. Because phi = 0 for clay
   Answer: A. With no cohesion intercept, sin phi equals radius over centre of the failure circle. (Key point: c = 0 for NC clay)

2. In the drained test, what is phi'?
   A. 22.6°
   B. 40.5°
   C. 27.5°
   D. 31.3°
   Answer: D. sigma_1' = 950, so sin phi' = 650/1250 = 0.52 and phi' = 31.3°. (Key point: Drained phi')

3. What is the total stress phi_cu for the CU test?
   A. 31.3°
   B. 15.0°
   C. 22.6°
   D. 38.2°
   Answer: C. sigma_1 = 450, sin phi_cu = 250/650 = 0.385, phi_cu = 22.6°. (Key point: CU total phi)

4. How is u_f found in the CU test?
   A. u_f = sigma_1 - sigma_3 = 250 kPa
   B. Use phi' = 31.3° with the effective circle (sigma_3' = 115.4) and u_f = sigma_3 - sigma_3' = 84.6 kPa
   C. u_f = 200 + 115.4 = 315.4 kPa
   D. u_f = 0 because the clay is NC
   Answer: B. Deviator stress is unchanged by pore pressure; effective sigma_3' = 115.4 so u_f = 200 - 115.4 = 84.6 kPa. (Key point: Pore pressure at failure)

## Related in Soil Mechanics

- [CU test on NC clay, three samples](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Acu-test-nc-clay-envelopes) — Soil Mechanics, chapter 10
- [CU test NC clay 200/350/80, φ and φ'](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Acu-nc-clay-200-350-80) — Soil Mechanics, chapter 10
- [CU tests on overconsolidated clay](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Acu-overconsolidated-effective-parameters) — Soil Mechanics, chapter 10
- [CU test: σ3 200, σ1 550, u 80](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Acu-test-failure-plane-direction) — Soil Mechanics, chapter 10
- [Triaxial tests by drainage; UCS vs cu](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Atriaxial-tests-by-drainage-ucs) — Soil Mechanics, chapter 10
- [Surcharge 15 kPa, stresses at clay centre](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Asurcharge-15kpa-stresses-clay-center) — Soil Mechanics, chapter 9

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