## Sheet Pile Wall Anchors in Granular Media: Stability Considerations

**Introduction**

Sheet piles are commonly used as anchor walls to withstand lateral loads. They derive their capacity

due to the resultant of passive and active pressure acting on the front and rear face of the wall under

the action of anchor pull. Many of the bulkhead failures are attributed to failure of their anchors. It is

important to ensure safety of the anchor units to protect the main structures they support.

When a wall is pulled by an anchor it tends to rotate about a pivot point and active and passive

pressures develop on the front and rear faces of the wall. When the pivot is at the tip of the wall the

resulting pressure distribution as per Rankine’s theory is shown in Fig.1.

For this wall movement it is necessary to apply the anchor pull at a depth equal to 2/3H where H is the height of the wall. The

anchor capacity Pu per unit length of wall is the given by

Where Ka and Kp, are active and passive earth pressure coefficients, ϒ is unit weight of soil. This also turns out to be the maximum capacity of the wall.

However, often in practice the tie location depends on other practical considerations. For instance, in the case of anchored sheet pile retaining wall the tie location in the main wall determines the location of the anchor in the wall. The height of the anchor wall depends on the required anchor capacity. The depth of the tie location *h* in the anchor wall below the ground level may not be equal to 2/3H. In such a case, the distribution of the earth pressure will get modified to ensure rotational equilibrium of the wall. We shall show that the anchor capacity will depend on the location of the tie in the wall. This problem which is of considerable importance from the design point of view of sheet pile wall anchors has not been dealt with adequately in the literature. Considering that a number of bulkhead failures are attributed to inadequate anchorage, development of rational procedures for arriving at the capacity of anchor for different tie locations assumes importance. We will consider only anchors in sand strata, though the method adopted is general and applicable clay and layered strata as well.

*General Tie Location *

Consider the anchor wall shown in Fig.2. Let *h* be the depth below the top of the wall at which tie is connected. The mode of failure of the wall will be by rotation about a pivot. We shall first consider the case in which the rotation of the wall is anticlockwise. Let *z* be the depth of the pivot point from the top of the pile. The Rankine pressure distribution on both sides of the wall recognising the switch in the distribution at the pivot point is shown in Fig.2. The depth *z* can be determined by invoking the condition of moment equilibrium. Taking moment about the anchor point we get

Using the notation *α = z/H* and

*the above equation-2 can be written as*

*β*= h/HFor any given value of *β* specifying the location of the tie, the value of α defining the location of the pivot could be obtained by solving equation-3. It is most convenient to obtain the solution numerically by iteration. The ultimate anchor capacity *P _{u}* can then be obtained from the horizontal equilibrium equation.

It may be easily verified that values of *α = 1 *satisfy Equation-1 when* β=2/3*. Let us now consider the case when *h > 2/3H*.

In this case the pivot would shift above 2/3H and the wall will tend to rotate in a clockwise direction about the pivot and the pressure distribution on the wall is shown in Fig.3.

It may be seen that the pressure distributions shown in Fig.2 and Fig.3 are similar except that the front and back side distributions have got interchanged. On account of this the moment equilibrium equation remains unchanged and Equation-3 can still be used to determine the value of *α * for a given value of * β*. Equation-4 with a change of sign on the right hand side can then be used to obtain the anchor capacity.

We may verify from Equation-4 for values of such that 0 ≤ *α *≤ 1the maximum value of *P _{u}* is obtained when

*We may thus conclude that*

*α*= 0 or 1.*β=2/3*yields maximum anchor capacity.

Solving equation-3 and equation-4 for values of * β *ranging from

*0 to 1,*values of

*α*and Pu are obtained and presented in Fig.4 and Fig.5 respectively.

The variation of * α* with

*is shown in Fig.4. It can be seen when the tie is located at the top of the pile that is when the value*

*β**the value of*

*=0.0**β**is*

*α**0.793*. As the value of

*increases, the value of*

*β**also increases and when*

*α**tends to 2/3 corresponding to the special tie location, the pivot reaches the pile tip. As the tie location just crosses and goes below the special tie location point the pivot flips to the top of the pile. Further increase in the value of*

*β**is accompanied by an increase in the value of*

*β**. For the tie location at the bottom of the pile i.e., for*

*α**the value*

*=1.0,**β**obtained is 0.5.*

*α*It can be seen when the tie is located at the top of the pile that is when the value * β* = 0.0 the value of a is 0.793 corresponding to a Pu value of only 0.26 P

_{umax}

As the value of * β* increases the value of

*also increases and when*

*α**tends to 2/3 the value of a tends to 1.0 and Pu reaches its maximum. When*

*β**just exceeds 2//3 the pivot flips to the top of the wall i.e.,*

*β**= 0. Pu at this stage is still at its maximum. With further increase of*

*α**,*

*β**also increases. When*

*α**touches a value of 1.0 i.e., load applied at the pile tip*

*β**= 0.5 and Pu also 1/2 of P*

*α*_{umax}.

**Concluding Remarks**

A method based on center of rotation concept is described for evaluating sheet pile anchor wall capacity. The capacity of the tie varies considerably depending on its location in the wall. In the light of the above results due consideration is warranted in the design procedures for sheet pile wall anchors. The method outlined is versatile in that cohesive and layered soil strata and water table depth can be considered.