Question 2 of 6: The three limit lateral earth pressures

Question 2: The three limit lateral earth pressures (10 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.

The lateral pressure a soil exerts on a wall depends on how much the wall moves relative to the backfill. Three limiting states are defined, each with a coefficient $K$ relating the horizontal effective stress to the vertical effective stress, $\sigma_h' = K\,\sigma_v'$.

At-rest ($K_0$). The wall does not move, so the backfill retains the lateral stress it had in the ground. For a normally consolidated soil Jaky's relation gives $K_0 = 1-\sin\phi'$ (for OC soil $K_0 = (1-\sin\phi')\,\mathrm{OCR}^{\sin\phi'}$). Because the soil is not at failure, the Mohr circle drawn between $\sigma_h'=K_0\sigma_v'$ and $\sigma_v'$ lies entirely inside the Mohr–Coulomb failure envelope.

Active ($K_a$). The wall moves away from the backfill; the soil expands laterally and the horizontal stress drops until the soil fails. The horizontal stress reaches its minimum,

Here $\sigma_v'$ is the major principal stress $\sigma_1$ and $\sigma_h'=K_a\sigma_v'$ is the minor $\sigma_3$; the Mohr circle is small and just touches (is tangent to) the failure envelope.

Passive ($K_p$). The wall is pushed into the backfill; the soil is compressed laterally and the horizontal stress rises to its maximum,

Now the roles reverse: $\sigma_h'=K_p\sigma_v'$ is the major principal stress and $\sigma_v'$ is the minor. The Mohr circle is the largest of the three and is again tangent to the failure envelope. Only a small wall movement mobilises the full active state, whereas a much larger movement is needed to develop the passive state.