---
title: "Uniform sand, water table 2 m, capillary"
subject: "Soil Mechanics"
chapter: 6
key: "semester_4/soil_mechanics:uniform-sand-effective-stress-capillary"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/uniform-sand-effective-stress-capillary
site: BCT Engineering
---

# Uniform sand, water table 2 m, capillary

Soil Mechanics · Chapter 6: Principle of Effective Stress, Capillarity and Permeability

- Asked in: 2079 Asoj, 8 marks
- Video: [Effective stress, Total stress and Pore water pressure in Soil Mechanics || Example solved](https://www.youtube.com/watch?v=5r3McEtuyXU) — Civil Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/uniform-sand-effective-stress-capillary
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-6

## Question

The water table in a deposit of uniform sand is located at 2 m below the ground surface. Assuming the soil above the water table is dry,
(i) Determine the effective stress at a depth of 5 m below the ground surface. Take bulk unit weight of sand as 18 kN/m³.
(ii) If the soil above the water table is saturated by capillary action, what is the effective stress at that depth?
Also plot the variation of total pressure and effective pressure over the depth of 5 m in both the cases.

## Short answer

Effective stress at 5 m depth is 60.57 kPa in both cases. Capillary saturation raises the effective stress only above the water table, by up to 19.62 kPa at the surface.

## Answer

#### Given

Uniform sand, water table (WT) at 2 m depth, $\gamma = 18$ kN/m³, $\gamma_w = 9.81$ kN/m³. Depth of interest = 5 m.

#### (i) Dry sand above the WT

- Total stress: $\sigma = 18 \times 5 = 90.0$ kPa
- Pore pressure at 5 m: $u = 9.81 \times (5-2) = 29.43$ kPa

$$
\sigma' = 90.0 - 29.43 = 60.57\ \text{kPa}
$$

Variation with depth (linear):

| Depth (m) | $\sigma$ | $u$ | $\sigma'$ |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 2 (WT) | 36.0 | 0 | 36.0 |
| 5 | 90.0 | 29.43 | 60.57 |

#### (ii) Sand above the WT saturated by capillary action

The pore water in the 2 m above the WT is under suction: $u = -\gamma_w z_c$, so $u = -19.62$ kPa at the ground surface (top of the capillary zone) and 0 at the WT. The soil weight is still taken as 18 kN/m³ (no other unit weight is given), so the total stress is unchanged.

At 5 m: $\sigma = 90.0$ kPa, $u = 29.43$ kPa, so

$$
\sigma' = 90.0 - 29.43 = 60.57\ \text{kPa}
$$

The effective stress at 5 m is the same as in (i): capillary suction changes the stress only within the capillary zone (and below it, if the saturated weight were larger).

| Depth (m) | $\sigma$ | $u$ | $\sigma'$ |
|---|---|---|---|
| 0 | 0 | $-19.62$ | 19.62 |
| 2 (WT) | 36.0 | 0 | 36.0 |
| 5 | 90.0 | 29.43 | 60.57 |

If the saturated unit weight were higher than 18 kN/m³ in the capillary zone, the total and effective stress below would increase by $(\gamma_{sat}-18)\times 2$.

#### Plot

```text
 Case (i)               Case (ii)
 σ' at 0 m = 0          σ' at 0 m = 19.6  (σ'-line shifts right
                                           above the WT)
 σ' at 2 m = 36         σ' at 2 m = 36
 σ' at 5 m = 60.6       σ' at 5 m = 60.6
```

**Answer: (i) $\sigma' = 60.57$ kPa. (ii) $\sigma' = 60.57$ kPa at 5 m; the effective stress is increased only in the top 2 m (by $\gamma_w z_c$, up to 19.62 kPa at the surface).**

## Check yourself

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

1. For dry sand above a WT at 2 m, the effective stress at 5 m is:
   A. 90 kPa
   B. 60.57 kPa
   C. 29.43 kPa
   D. 36 kPa
   Answer: B. sigma = 18 x 5 = 90; u = 9.81 x 3 = 29.43; sigma' = 60.57 kPa. (Key point: Case (i) method)

2. With full capillary saturation up to the surface, u at the ground surface is:
   A. +19.62 kPa
   B. 0
   C. -19.62 kPa
   D. -9.81 kPa
   Answer: C. u = -gamma_w z_c with z_c = 2 m, giving -19.62 kPa. (Key point: Capillary pore pressure)

3. With capillary saturation (same 18 kN/m3 weight), sigma' at 5 m is:
   A. 80.19 kPa
   B. 40.95 kPa
   C. 60.57 kPa, unchanged
   D. 90 kPa
   Answer: C. Suction only changes u inside the capillary zone; at 5 m, sigma and u are unchanged. (Key point: Case (ii) result)

4. Capillarity increases effective stress:
   A. Everywhere below the WT
   B. Only within the capillary zone above the WT (up to 19.62 kPa at the surface)
   C. Only at the WT
   D. Only below 5 m
   Answer: B. sigma' rises by gamma_w z_c within the capillary zone only. (Key point: Where capillarity acts)

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