Effective Stress Through Excavation and Fill Placement: 22-Agric-A2 Soil Physics and Mechanics, May 2014, Q4

Question 4: Effective Stress Through Excavation and Fill Placement (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Quantity	Value
Original water table depth	4 m below surface
Native soil unit weight, above WT	16.7 kN/m³
Native soil unit weight, below WT (saturated)	19.9 kN/m³
Fill unit weight	16.0 kN/m³
Excavation depth (stage 1)	3 m, over a large area
Fill thickness (stage 2)	6 m, over the same large area
Point B	on the water table (fixed elevation, 4 m below the original surface)
Point A	10 m below the water table (fixed elevation) in every stage

Find. Total stress σ, pore pressure u and effective stress σ′ at points A and B, at three times: initial, after excavation, and immediately after fill placement.

Approach. Because the excavation and fill are spread over "a large area," treat the loading as one-dimensional (no lateral stress spreading): every added or removed overburden layer changes total stress uniformly with depth below it. The water table's elevation is controlled regionally and does not move with a local excavation/fill, so hydrostatic pore pressure is always measured from that fixed elevation, except immediately after the fill is placed: because the native soil is "poorly drained" (a saturated fine-grained/cohesive material), the fill load is carried initially as excess pore pressure ($\Delta u \approx \Delta\sigma$, undrained response, Terzaghi's principle) rather than by the soil skeleton, so effective stress is momentarily unchanged from its after-excavation value.

Three construction stages. B always sits on the water table; A is always 10 m below it. After excavation, only 1 m of native soil remains above the (unmoved) water table; after fill placement the new ground surface sits 3 m above the original grade.

Stage 1 — initial condition. B is 4 m below the original surface, in soil at $\gamma = 16.7\ \text{kN/m}^3$ (above WT, so u = 0 there); A is a further 10 m below, in saturated soil at $\gamma = 19.9\ \text{kN/m}^3$: $$\sigma_B = 16.7(4) = \boxed{66.8\ \text{kPa}}, \quad u_B = 0, \quad \sigma_B' = 66.8\ \text{kPa}$$ $$\sigma_A = 16.7(4) + 19.9(10) = \boxed{265.8\ \text{kPa}}, \quad u_A = \gamma_w(10) = 9.81(10) = 98.1\ \text{kPa}, \quad \sigma_A' = 265.8 - 98.1 = \boxed{167.7\ \text{kPa}}$$
Stage 2 — after excavation of the top 3 m. The water table's elevation is unchanged, so only $4-3=1\ \text{m}$ of native soil now overlies it at the new surface; pore pressure re-equilibrates to the ordinary hydrostatic profile from the (unmoved) water table: $$\sigma_B = 16.7(1) = \boxed{16.7\ \text{kPa}}, \quad u_B = 0, \quad \sigma_B' = 16.7\ \text{kPa}$$ $$\sigma_A = 16.7(1) + 19.9(10) = \boxed{215.7\ \text{kPa}}, \quad u_A = 98.1\ \text{kPa}, \quad \sigma_A' = 215.7 - 98.1 = \boxed{117.6\ \text{kPa}}$$ Both points lose effective stress on unloading — exactly the mechanism (stress relief) that motivates a later surcharge fill to pre-load the ground.
Stage 3 — immediately after fill placement. The 6 m fill adds a uniform total stress increment $\Delta\sigma = \gamma_{\text{fill}}(6) = 16.0(6) = 96.0\ \text{kPa}$ at every depth below it. Because the underlying native soil is poorly drained (saturated, low permeability), this load has no time to drain immediately after placement, so it is carried entirely as excess pore pressure ($\Delta u = \Delta\sigma$): $$\sigma_B = 16.7 + 96.0 = \boxed{112.7\ \text{kPa}}, \quad u_B = 0 + 96.0 = 96.0\ \text{kPa}, \quad \sigma_B' = 112.7 - 96.0 = \boxed{16.7\ \text{kPa}}\ (\text{unchanged from Stage 2})$$ $$\sigma_A = 215.7 + 96.0 = \boxed{311.7\ \text{kPa}}, \quad u_A = 98.1 + 96.0 = 194.1\ \text{kPa}, \quad \sigma_A' = 311.7 - 194.1 = \boxed{117.6\ \text{kPa}}\ (\text{unchanged from Stage 2})$$ Effective stress at both points is momentarily the same as right after excavation — the fill's entire weight is initially held up by the pore water, and only dissipates into the soil skeleton (raising σ′, and with it strength) as the excess pore pressure drains away over time.

Stage	σ_B	u_B	σ′_B	σ_A	u_A	σ′_A
1. Initial	66.8	0	66.8	265.8	98.1	167.7
2. After excavation	16.7	0	16.7	215.7	98.1	117.6
3. Immediately after fill	112.7	96.0	16.7	311.7	194.1	117.6
All values in kPa (kN/m²)

Concept & Theory

Topic: Terzaghi's effective stress principle and the undrained response of saturated fine-grained soil to a rapid load.

Key relations: $\sigma' = \sigma - u$; immediately after a rapid (undrained) load change on saturated soil, $\Delta u \approx \Delta\sigma$ (Skempton's B ≈ 1 for a saturated, fine-grained soil).

Why this works: A saturated, poorly drained soil cannot expel or draw in water fast enough to accommodate a sudden load change, so the incompressible pore water initially takes up essentially all of the added stress; only as excess pore pressure dissipates by seepage (consolidation) does the soil skeleton pick up the load and effective stress — and with it, strength — rise toward its final, drained value.

Common pitfall: Assuming pore pressure is always simply hydrostatic from current ground level, which misses both that the water table's absolute elevation (not depth below whatever surface exists at the time) sets the hydrostatic datum, and that an undrained load produces an *excess* pore pressure on top of the hydrostatic value that has not yet had time to dissipate.

Source: R.F. Craig, Craig's Soil Mechanics, 9th ed., Ch. 3 (effective stress); B.M. Das, Principles of Geotechnical Engineering, 9th ed., Ch. 3, 11 (effective stress, consolidation).

Question 4 of 7: Effective Stress Through Excavation and Fill Placement

Question 4: Effective Stress Through Excavation and Fill Placement (20 marks)