## STABILITY OF FLEXIBLE RETAINING WALLS

Sheet pile walls are fl exible and are constructed using steel or thin concrete panels or wood. Two types of sheet pile walls are common. One is a cantilever wall, commonly used to support soils to a height of less than 3 m (Figure). The other is an anchored or propped sheet pile wall (Figure ), commonly used to support deep excavations and as waterfront retaining structures. Cantilever sheet pile walls rely on the passive soil resistance for their stability, while anchored sheet pile walls rely on a combination of anchors and passive soil resistance for their stability. The stability of sheet pile walls must satisfy all the criteria for rigid retaining walls described in Section. Because sheet pile walls are used in situations where seepage may occur, it is necessary to pay particular attention to seepage-related instabilities.

**Analysis of Sheet Pile Walls in Uniform Soils:**

In analyzing sheet pile walls, we are attempting to determine the depth of embedment, d, for stability. The analysis is not exact, and various simplifi cations are made. The key static equilibrium condition is moment equilibrium. Once we determine d, the next step is to determine the size of the wall. This is done by calculating the maximum bending moment and then determining the section modulus by dividing the maximum bending moment by the allowable bending stress of the material constituting the sheet pile, for example, steel, concrete, or wood.

An effective stress analysis is generally used to analyze sheet pile walls, and as such we must evaluate the porewater pressure distribution and seepage pressures. We can use fl ownet sketching or numerical methods to determine the porewater pressure distribution and seepage pressures. However, approximate methods are often used in practice. If the groundwater level on both sides of a sheet pile wall is the same, then the resultant porewater pressures and seepage pressures are zero (Figure ). You can then neglect the effects of groundwater in determining the stability of sheet pile walls. However, you must use effective stresses in your calculations of the lateral earth forces.

The approximate distribution of porewater pressures in front of and behind sheet pile walls for conditions in which the water tables are different is obtained by assuming a steady-state seepage condition and uniform distribution of the total head. Approximate resultant porewater pressure distributions for some common conditions (Padfi eld and Mair, 1984) are shown in Figure .

Approximate resultant porewater pressure

distribution behind fl exible retaining walls.

The maximum porewater pressures (uB), maximum porewater forces (Pw) and their locations 1zw2, and the seepage force per unit volume (js) are as follows:

**Case (a)**

Resultant porewater pressure is zero and the seepage force is zero.

**Case (b)**

**Case (c)**

Recall that js is the seepage pressure per unit volume, and the resultant effective stress is increased when seepage is downward (behind the wall) and is decreased when seepage is upward (in front of the wall).