Total & Effective Stress Before and Immediately After Fill Placement: 18-Env-A3 Geotechnical and Hydrogeological Engineering, December 2014, Q4

Question 4: Total & Effective Stress Before and Immediately After 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.

Given data
Quantity	Symbol	Value
Stiff silty clay: thickness, unit weight	$H_1$, $\gamma_1$	7.0 m, 19.0 kN/m³
Very stiff clay: thickness, unit weight	$H_2$, $\gamma_2$	18.0 m, 19.5 kN/m³
Proposed fill: thickness, unit weight	$H_f$, $\gamma_f$	8.5 m, 20.3 kN/m³
Groundwater table	—	at original ground surface
Point A depth (within silty clay)	$z_A$	4.0 m below original ground surface
Point B depth (10 m into very stiff clay)	$z_B$	7.0 + 10.0 = 17.0 m below original ground surface

Find. (a) total stress $\sigma$ and effective stress $\sigma'$ at A and B before the fill; (b) total stress, pore pressure $u$ and effective stress at A and B immediately after the fill is placed.

Approach. Sum $\gamma\times$thickness down to each point for the pre-fill total stress and subtract hydrostatic pore pressure (GWT at surface) for effective stress; then apply the fill as an instantaneous, undrained surcharge — a saturated clay carries the entire freshly-applied load as excess pore pressure at $t=0^+$, so total stress and pore pressure both rise by the surcharge while effective stress is momentarily unchanged.

Figure 2. Depths on the left scale are measured from the original ground surface (top of the fill, once placed); points A and B are shown at their true depths within the silty clay and very stiff clay layers.

Part (a) — point A, before fill. $\sigma_A=\gamma_1z_A=19\times4.0=76.00\ \text{kPa}$; $u_A=\gamma_wz_A=9.81\times4.0=39.24\ \text{kPa}$; $$\sigma_A'=\sigma_A-u_A=76.00-39.24=\boxed{36.76\ \text{kPa}}.$$
Part (a) — point B, before fill. $\sigma_B=\gamma_1H_1+\gamma_2(10.0)=19\times7+19.5\times10=328.00\ \text{kPa}$; $u_B=\gamma_wz_B=9.81\times17.0=166.77\ \text{kPa}$; $$\sigma_B'=328.00-166.77=\boxed{161.23\ \text{kPa}}.$$
Fill surcharge. The fill applies a uniform surcharge at every depth in the profile beneath it (one-dimensional loading under a wide fill): $$\Delta\sigma=\gamma_fH_f=20.3\times8.5=172.55\ \text{kPa}.$$
Part (b) — immediately after fill (undrained response). A saturated clay cannot drain instantly, so ALL of the freshly-applied surcharge appears as excess pore pressure at $t=0^+$ ($\Delta u=\Delta\sigma$), and effective stress is unchanged: $$\sigma_{A,1}=76.00+172.55=248.55\ \text{kPa},\quad u_{A,1}=39.24+172.55=211.79\ \text{kPa},\quad \sigma_{A,1}'=\boxed{36.76\ \text{kPa}}\ (\text{unchanged}).$$ $$\sigma_{B,1}=328.00+172.55=500.55\ \text{kPa},\quad u_{B,1}=166.77+172.55=339.32\ \text{kPa},\quad \sigma_{B,1}'=\boxed{161.23\ \text{kPa}}\ (\text{unchanged}).$$

Check: assumes Skempton's pore-pressure parameter $B\approx1$ for the saturated clay under undrained, one-dimensional loading, so the excess pore pressure exactly equals the applied surcharge immediately after placement — effective stress only begins to rise later, as consolidation dissipates this excess pressure over time.

Point / condition	$\sigma$ (kPa)	$u$ (kPa)	$\sigma'$ (kPa)
A, before fill	76.00	39.24	36.76
B, before fill	328.00	166.77	161.23
A, immediately after fill	248.55	211.79	36.76 (unchanged)
B, immediately after fill	500.55	339.32	161.23 (unchanged)

Concept & Theory

Topic. Total stress, pore pressure and effective stress response of saturated clay to a rapidly-applied surcharge.

Key relations. $\sigma'=\sigma-u$; $\sigma=\sum\gamma h$; undrained loading $\Delta u=\Delta\sigma$ (Skempton $B=1$, 1-D loading).

Why this works. Terzaghi's effective stress principle states that only effective stress controls soil strength and deformation. A wide, rapidly-placed surcharge over a saturated, low-permeability clay cannot drain in the time it takes to place it, so the added load is initially carried entirely by the pore water; effective stress — and therefore settlement and strength gain — only develops later as consolidation dissipates the excess pore pressure.

Common pitfall. Assuming effective stress rises immediately with the fill (forgetting the undrained response); forgetting to add the fill surcharge at EVERY depth in the profile rather than only at the ground surface.

Source. Das, Principles of Geotechnical Engineering, ch. 4 & 10 (effective stress; consolidation); Craig & Knappett, Craig's Soil Mechanics, effective stress and consolidation chapters.

Question 4 of 6: Total & Effective Stress Before and Immediately After Fill Placement

Question 4: Total & Effective Stress Before and Immediately After Fill Placement (20 marks)