# Retaining Walls: Are You Calculating the Passive Pressure Correctly?

September 23, 2019

Retaining walls are structures designed to bound soils between two different elevations, therefore they are mainly exposed to lateral pressures from the retained soil plus any other surcharge. In addition to the friction at the base, most retaining walls rely on the passive pressure at the front of the wall to prevent sliding problems. This article discusses the factors that may affect the calculation of the passive pressure in a retaining wall design. Our software ASDIP RETAIN will be used to support the discussion.

## What exactly is the passive pressure?

When the wall pushes laterally against the soil mass at the front, the soil is forced to develop its available full shear resistance. In other words, the passive state is the maximum lateral resistance that a given soil mass can offer to a retaining wall that is being pushed towards the soil. The passive pressure coefficient Kp is defined as the ratio of the horizontal to vertical stress. The image below shows schematically the pressure states of a soil mass, as well as the Rankine formula of Kp for granular soils, where ϕ is the internal friction angle. Note the maximum stress level corresponding to the passive state.

## How do you calculate the passive pressure?

The passive resistance is the area of the passive pressure diagram, which is a triangle. If the distance from the top of the front soil to the bottom of the shear key is H, then the pressure at the base is Kp*γ*H, where γ is the soil density. A factor that really affects the calculation of the passive pressure is the presence of the water table. In this case the submerged density of the soil γ' should be used in the calculation, in addition to the hydrostatic pressure, as shown below. Ignoring the water table in the calculations will produce unconservative results.

The passive pressure at the top of the diagram sometimes is ignored conservatively in the calculations, because it's unlikely that this portion of the soil remains undisturbed during or after the construction of the wall, as shown above. Note that the bottom of the passive diagram coincides with the bottom of the shear key. ASDIP RETAIN includes all these factors in the passive pressure calculation.

## Takeaway

ASDIP RETAIN is a tool for design of retaining walls, with multiple options to optimize the design easily. The calculation of the passive pressure may be affected by external factors, such as the presence of the water table. The disturbed top portion of the passive diagram is sometimes conservatively ignored in the calculations.

Detailed information is available about this structural engineering software by visiting ASDIP RETAIN. For a discussion of the sliding failure mode see the post Cantilever Retaining Walls: How to Calculate the Sliding Safety Factor. For our collection of blog posts about retaining walls please visit Structural Retaining Wall Design.