Question 6 of 6: Undrained strength beneath an embankment from Skempton pore pressures

Question 6: Undrained strength beneath an embankment from Skempton pore pressures (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. Fill density $\rho_{fill}=1.7$ Mg/m³; foundation soil $c'=50$ kPa, $\phi'=21^\circ$; Skempton $A=0.2$, $B=0.98$; fill raised from 3 m to 6 m undrained; lateral stress increase $=\tfrac12$ vertical increase.

Find. The undrained shear strength $s_u$ of the foundation soil below the embankment centre immediately after raising the fill; and whether the soil is normally or over-consolidated.

Approach. Compute the vertical stress increase from the added fill, take the horizontal increase as one-half of it, obtain the excess pore pressure from Skempton’s equation, then find the effective vertical stress just after loading and the corresponding undrained shear strength from the effective-stress envelope.

1. Fill unit weight and vertical stress increase. With $\gamma_{fill}=(1.7)(9.81)=16.68\ \text{kN/m}^3$ and 3 m of new fill, $$\Delta\sigma_1 = \gamma_{fill}\,\Delta h = (16.68)(3) = 50.0\ \text{kPa}.$$
2. Horizontal stress increase. As instructed, the lateral increase is half the vertical: $$\Delta\sigma_3 = \tfrac12\,\Delta\sigma_1 = 25.0\ \text{kPa}.$$
3. Excess pore pressure (Skempton). $$\Delta u = B\big[\Delta\sigma_3 + A(\Delta\sigma_1 - \Delta\sigma_3)\big] = 0.98\big[25.0 + 0.2(25.0)\big] = 0.98(30.0) = \boxed{29.4\ \text{kPa}}.$$
4. Effective vertical stress just after loading. Following the standard treatment of this problem (Craig), the pore pressure is taken as zero at the start of the raise, i.e. the first 3 m of fill is treated as consolidated, and the stated negligible dissipation applies to the pore pressure generated by the 3 m to 6 m raise. Only that excess $\Delta u$ is acting. The total vertical stress from the full 6 m fill (taken at the foundation surface below the centre) is $(16.68)(6)=100.1$ kPa, hence $$\sigma'_v = 100.1 - 29.4 = 70.6\ \text{kPa}.$$
5. Undrained shear strength. On the (approximately horizontal) shear surface below the centre, the effective-stress envelope gives $$s_u = c' + \sigma'_v\tan\phi' = 50 + (70.6)\tan 21^\circ = 50 + 27.1 = \boxed{77.1\ \text{kPa}}.$$
6. Normally or over-consolidated? The soil is over-consolidated. Two independent indicators agree: (a) the effective-stress envelope has a real cohesion intercept $c' = 50$ kPa — a normally consolidated clay has $c'\approx0$ (envelope through the origin); and (b) the pore-pressure parameter $A = 0.2$ is low ($<0.5$), the dilatant signature of an over-consolidated soil, whereas a NC clay gives $A_f \approx 0.5$–$1.0$.