Before the surcharge, what are the total and pore pressure at 11 m?

Total 207 kPa and pore pressure 90 kPa

Total 207 kPa and pore pressure 110 kPa

Total 117 kPa and pore pressure 90 kPa

Total 207 kPa and pore pressure 0

Immediately after the sudden 15 kPa load, who carries it?

The pore water; excess pore pressure is 15 kPa and effective stress stays 117 kPa

The soil skeleton; effective stress becomes 132 kPa

It is shared equally by water and soil

Nobody; stresses stay unchanged

What are the pore pressure and effective stress long after loading?

Pore pressure 90 kPa and effective stress 132 kPa

Pore pressure 105 kPa and effective stress 117 kPa

Pore pressure 90 kPa and effective stress 117 kPa

Pore pressure 0 and effective stress 222 kPa

2073 Magh · 5 marks

Surcharge 15 kPa, stresses at clay centre

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.

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.

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.

✓ Answer checked by Claude Opus 5.5 (high effort)

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Surcharge 15 kPa, stresses at clay centre

(i) Before applying the surcharge

(ii) Immediately after applying the surcharge

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

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