## Loads and Forces Acting on Retaining Wall

There are various types of loads and forces acting on retaining wall, which are:

- Lateral earth pressure
- Surcharge loads
- Axial loads
- Wind on projecting stem
- Impact forces
- Seismic earth pressure
- Seismic wall self-weight forces

Retaining wall design could include any or all of loads and forces which are explained in the following sections:

**1. ****Lateral Earth Pressure Acting on Retaining Wall**

The main purpose of retaining wall construction is to retain soil that is why soil lateral earth pressure is major concern in the design. Sliding soil wedge theory is the basis for most of theories by which lateral earth pressure is computed.

The wedge theory suggests that a triangular wedge of soil would slide down if retaining wall was removed suddenly and the wall has to sustain this wedge soil. Figure 1 shows free body lateral forces acting on retaining walls.

**Figure-1: Free body of lateral forces acting on retaining wall**

Coulomb and Rankine equations are two major formulas which are used to compute lateral earth pressure:

**The Coulomb method of Lateral Earth Pressure Calculation**

This equation takes backfill slope, friction angle at wall face, rupture plan angle, and internal friction angle into consideration:

**Where:**

*Ka***: **Coefficient of active pressure

: Angle of internal friction

: Angle of backfill slope

: Angle of friction between soil and wall (2?3 to 1?2 is assumed)

: Slope angle of the wall which is measured from horizontal (equal to 90 degree for vertical wall)

Furthermore, in the case of flat level backfill soil, considering zero friction at soil-wall interface, and soil-sidewall is vertical, the** coulomb equation** is reduced to the following:

**The Rankine method of Lateral Earth Pressure Calculation**

This equation, which derived by William Rankine, is the development of coulomb formula. The Rankine method does not take the friction between wall and soil into account.

This makes it a conservative way for designing retaining walls. The Rankine lateral earth pressure equation is the same for both zero-wall friction and level backfill soil:

Where:

: Backfill slope angle

: Internal friction angle of soil

**Rankine equation is rearranged when backfill is level as:**

**2. ****Surcharge loads Acting on Retaining Wall**

Surcharge loads acting on retaining wall are additional vertical loads that used to the backfill soil above the top of the wall. It can be either dead loads for example sloping backfill above the wall height or live load which could result from highway or parking lot, paving or adjacent footing.

Live load surcharge is considered when vehicular actions act on the surface of backfill soil at a distance which equal or less than the wall height from the wall back face. Active pressure from uniform surcharge is explained in the Figure 2.

**Figure-2: Active pressure from a uniform surcharge against the retaining wall**

Where:

: is the density of soil

*W*: is the uniform surcharge load

*H*: is the height of the wall

*P _{1}=K_{a} WH* –> Equation 7

*P _{2}=0.5K_{a}H^{2}* –>Equation 8

**There are various types of surcharge loads such as:**

- Highway surcharges
- Backfill compaction surcharge
- Adjacent footing surcharge

**3. Axial Forces Acting on Retaining Wall**

Overturning resistance on retaining wall is provided by axial loads. There are different types of axial load that will be discussed in the following sections:

**a) ****Vertical loads on the stem**

These loads might be resulted from beam reactions, bridge, or lodger and applied to the stem directly.

For most critical conditions, it is not necessary to consider live load from dead load separately because axial live load on the stem increases resisting moments and soil bearing pressure.

Point vertical loads on walls are considered to be spread downward in a slope of two vertical to one horizontal. Consequently, there will be rather low compressive stresses at the base of the wall, girder reactions on walls is an example of vertical point load.

Moreover, bearing stresses that directly under girder or beams reactions must be checked in addition to take eccentricity into account with respect to the stem centerline since it influences stability and design of the stem.

Finally, it is worth mentioning that, un-conservative results might be produced by acting live loads at negative eccentricity toward backfill.

**b) ****Soil weight**

It is the weight of the soil above toe and heel of the retaining wall.

**c) ****Structural weight**

It includes weight of the footing and stem which added to the bearing pressure of the soil and help stability against sliding and overturning.

**d) ****Vertical component of active pressure**

It is another vertical load, resultant earth pressure action line is at an angle from horizontal provided that backfill soil is sloped.

The angle is equal to the backfill slope angle according to Rankine formula and is the same as soil-stem friction angle according to coulomb formula. This inclined active pressure has two components includes horizontal and vertical.

The latter is employed as added sliding resistance, decrease soil pressure, and increase withstand against overturning.

**4. Wind Forces on Projecting Stem**

Wind pressure generates an overturning force when retaining wall is exposed and extends above grade. Common formula used to compute wind pressure is as follow:

*F=0.0026V ^{2}* –> Equation 9

**Where:**

*F*: wind pressure

*V*: Velocity of the wind

According to ASCE 7 design wind pressure (F) is calculated using the following simplified formula:

*F=q _{z} GG_{f}* –> Equation 10

**Where:**

*G*: is the gust factor (0.85 can be used)

*G _{f}:* Commonly taken as 1.2

*q _{z}*: is the velocity pressure at mid height and can be calculated using the following formula:

*q _{z}=0.613K_{z} K_{zt} K_{d} V^{2}* –> Equation 11

**Where:**

*K _{z}*: wind directionality factor, can be determined in section 26.6 of ASCE 7-10

*K _{zt}*: Velocity pressure exposure coefficient, can be determined section 26.6 of ASCE 7-10

*K _{d}*: Topographic factor see section, can be determined 26.6 of ASCE 7-10

*V*: Basic wind speed in m/s

**5. ****Impact loads Acting on Retaining Wall**

Design retaining wall for car bumper might be necessary when the wall extends above grade and parking area is close to it. When retaining wall is designed for impact loads, the stem should be checked at equally spaced points along stem length from top to the bottom as impact load spread at the greater length of the stem. Moreover, use slope of two vertical to one horizontal for spreading impact load.

**Forces related to earthquake is covered in seismic design of retaining wall.**