---
title: "Surcharge 15 kPa, stresses at clay centre"
subject: "Soil Mechanics"
chapter: 9
key: "semester_4/soil_mechanics:surcharge-15kpa-stresses-clay-center"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/surcharge-15kpa-stresses-clay-center
site: BCT Engineering
---

# Surcharge 15 kPa, stresses at clay centre

Soil Mechanics · Chapter 9: Compressibility of Soil

- Asked in: 2073 Magh, 5 marks
- Video: [Calculating the Effective Stress at the Centre of a Clay Layer - Soil Mechanics](https://www.youtube.com/watch?v=c-91x45DdGA) — AF Math & Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/surcharge-15kpa-stresses-clay-center
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-9

## Question

A surcharge load of 15 kPa was applied on the ground surface having the soil profile as shown in the figure below. Consolidation settlement took place in the clay layer. A consolidation test was done for the clay layer and the following results were obtained: coefficient of consolidation, $c_v$ = $3.25 \times 10^{-7}$ m²/s, compression index, $C_c$ = 1.2 and coefficient of permeability, k = $3.5 \times 10^{-9}$ m/s. Assume that the consolidation of the clay layer is solely due to the change in stress at the center of the clay layer. Also, consider that there is no change in ground water level before and after the consolidation. Take $\gamma_w$ = 10 kN/m³. [Figure: surcharge 15 kN/m²; sand layer γ = 18 kN/m³ from 0 to 2 m (water table at 2 m); sand layer $\gamma_{sat}$ = 20 kN/m³ from 2 to 8 m; clay layer $\gamma_{sat}$ = 17 kN/m³, $e_0$ = 2.4 from 8 to 14 m; sand layer below 14 m.] Determine the total, effective and pore water pressure at the center of the clay layer (i) before applying the surcharge load, (ii) immediately after applying the surcharge load and (iii) sufficiently long after applying the surcharge load.

## Short answer

Before loading: total stress 207 kPa, pore pressure 90 kPa, effective stress 117 kPa. Immediately after: total 222 kPa, pore pressure 105 kPa, effective 117 kPa. Long after: total 222 kPa, pore pressure 90 kPa, effective 132 kPa.

## Answer

**Given:** centre of clay is at 11 m depth (clay 8 m to 14 m). Water table at 2 m. $\gamma_w = 10$ kN/m³. Sand above the water table: 18 kN/m³; saturated sand: 20 kN/m³; clay: 17 kN/m³.

**Total vertical stress at 11 m** before loading:

$$
\sigma_0 = 18(2) + 20(6) + 17(3) = 36 + 120 + 51 = 207\ \text{kPa}
$$

**Hydrostatic pore pressure:** $u_0 = 10 \times (11-2) = 90$ kPa.

#### (i) Before applying the surcharge

| | Value (kPa) |
|---|---|
| Total stress $\sigma$ | 207 |
| Pore pressure $u$ | 90 |
| Effective stress $\sigma' = \sigma - u$ | 117 |

#### (ii) Immediately after applying the surcharge

The clay is saturated and the load is applied suddenly, so the entire 15 kPa is carried by the water (excess pore pressure $\Delta u = 15$ kPa).

| | Value (kPa) |
|---|---|
| Total stress $\sigma = 207 + 15$ | 222 |
| Pore pressure $u = 90 + 15$ | 105 |
| Effective stress $\sigma'$ | 117 |

#### (iii) Sufficiently long after loading (end of consolidation)

The excess pore pressure has fully dissipated ($\Delta u = 0$), so the load is carried by the soil skeleton.

| | Value (kPa) |
|---|---|
| Total stress $\sigma$ | 222 |
| Pore pressure $u$ | 90 |
| Effective stress $\sigma' = 222 - 90$ | 132 |

**Answer:** effective stress is 117 kPa at the start and rises to 132 kPa at the end of consolidation; pore pressure goes 90, then 105, then 90 kPa.

## Check yourself

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

1. Before the surcharge, what are the total and pore pressure at 11 m?
   A. Total 207 kPa and pore pressure 110 kPa
   B. Total 207 kPa and pore pressure 90 kPa
   C. Total 117 kPa and pore pressure 90 kPa
   D. Total 207 kPa and pore pressure 0
   Answer: B. Total = 18(2)+20(6)+17(3) = 207 and u = 10 x (11 - 2) = 90 kPa. (Key point: Initial total and pore pressure)

2. Immediately after the sudden 15 kPa load, who carries it?
   A. The soil skeleton; effective stress becomes 132 kPa
   B. The pore water; excess pore pressure is 15 kPa and effective stress stays 117 kPa
   C. It is shared equally by water and soil
   D. Nobody; stresses stay unchanged
   Answer: B. In saturated clay the load is applied faster than water can drain, so water takes it all at first. (Key point: Immediately after loading)

3. What are the pore pressure and effective stress long after loading?
   A. Pore pressure 105 kPa and effective stress 117 kPa
   B. Pore pressure 90 kPa and effective stress 117 kPa
   C. Pore pressure 90 kPa and effective stress 132 kPa
   D. Pore pressure 0 and effective stress 222 kPa
   Answer: C. Excess pressure fully dissipates, so u returns to hydrostatic 90 kPa and effective stress is 222 - 90 = 132 kPa. (Key point: After consolidation)

4. Which relation is used throughout?
   A. sigma' = sigma + u
   B. sigma' = u - sigma
   C. sigma' = sigma x u
   D. sigma' = sigma - u
   Answer: D. Terzaghi's effective stress principle: effective equals total minus pore water pressure. (Key point: Effective stress relation)

## Related in Soil Mechanics

- [Primary settlement, sand over clay, 110 kPa](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aprimary-settlement-sand-clay-110kpa) — Soil Mechanics, chapter 9
- [Settlement with preconsolidation 125 kPa](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aprimary-consolidation-settlement-preconsolidated) — Soil Mechanics, chapter 9
- [Clay 10 m, 2.54 cm sample, half settlement](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aclay-10m-half-settlement-time-ratio) — Soil Mechanics, chapter 9
- [5 m clay, Cc 0.25, 65% consolidation](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aclay-5m-cc-025-65-percent) — Soil Mechanics, chapter 9, asked 2×
- [Time-settlement curve, 3 m clay](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Atime-settlement-curve-3m-clay) — Soil Mechanics, chapter 9
- [Final settlement of clay, +30 kN/m²](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Afinal-settlement-sand-clay-30kpa) — Soil Mechanics, chapter 9

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