Stability Calculation of Retaining Wall

Stability Checks for Retaining Walls

Overturning and sliding checks are done to make sure the stability of retaining walls. In addition to to this base bearing pressure is also checked to confirm whether it is within the limit. In this calculation we are concentrating on the two stability checks of sliding and over turning.

Assumptions

• Friction angle of soil 30
• Friction coefficient between soil and concrete 0.5
• Dry density of soil 18 kN/m³
• Water table is not consider for this calculation(If water pressure is considered, we have to consider the submerge unit weight of the soil and also need to consider the saturated unit weigh of the soil depending to capillary action of the soil.
• No surcharge load is considered to simplify the calculation

Active soil pressure                = (1 - Sinϕ) / (1 + Sinϕ)
                                                = (1 - Sin30) / (1 + Sin30)
                                                = 0.333

Passive soil pressure               = (1 + Sinϕ) / (1 - Sinϕ)
                                                = (1+ Sin30) / (1 - Sin30)
                                                = 3.0

Check for Overturning

Pressure at base                      = K_a γ h
                                                 = 0.333x18x3.9
                                                 = 23.377 kN/m²

Lateral Force                            = 0.5x23.377x3.9
                                                 = 45.584 kN

Soil weigh on foundation          = 2.6x3.4x18
                                                 = 159.12 kN

If retaining wall is over turned, it will rotate around the point "A". Therefor take moment around point 'A' to find the overturning moment and restoring moment.

Overturning Moment                 = 45.584 x 3.9 / 3
                                                  = 59.259 kNm

Restoring Moment                     = 159.12 x (2.6/2 +0.4)
                                                  = 270.504 kNm

Actual Factor of Safety              = 270.504 / 59.259
                                                  = 4.565
It should be noted that the weight of the structure has not been considered in this calculation. Even without the weight of the structure, there is a higher restoring moment. 
Factor of safety against sliding is generally considered as 1.5. However, it could be vary depending on the design requirements. Here, the value is well above the required value. Therefore, it can conclude as overturning check is satisfactory.

Check of Sliding

Sliding can be consider in two ways. Friction force between soil and concrete or passive pressure generated by a shear key can be considered to avoid the sliding of the structure.

Case 01 : No shear key, consider only friction between soil and concrete
Weight of the structure should be considered for this calculation as it increase the reaction that lead to higher friction force.

Density of concrete                 = 24 kN/m³
Weight of the structure            = (3.9x0.4 + 2.6x0.5)x24
                                                = 68.64 kN

Total weight                            = weight of soil + weight of structure
                                               = 159.12 + 68.64
                                               = 227.76 kN

Assume friction coefficient between soil and concrete as 0.5. This value may be vary depending on the ground condition.

Friction force                           = 0.5 x 227.76
                                                = 113.88 kN

Lateral force                            = 45.584 kN

Factor of safety                       = 113.88 / 45.584
                                                = 2.5

Generally, we keep the factor of safety around 1.5 against sliding. Actual safety factor is well above the allowable value. Therefore sliding is ok.

Case 02 : Providing Shear Key
Some of the engineers are reluctant to use the friction force along to avoid the sliding of retaining walls as the ground conditions could be vary and unpredictable. In addition, when the height of the retaining wall is increasing, effect of the passive pressure is considered most of the time. Even though the above calculation is satisfactory for sliding, we could proceed with this method also to get an idea about the concept.

Height of the shear key can be determine as follows

Factor of safety                      = Allowable sliding force / Actual sliding force
Allowable sliding force           = FOS (actual sliding force)

0.5 (K_p γ h) h                          = 1.5 x 45.584  
                    h²                       = 1.5 x 45.584 / (0.5 K_p γ)
                                               = 1.5 x 45.584 / (0.5x3x18)      
                                               = 2.532
                    h                         = 1.6 m

1.6 m height soil layer is required to generate above passive pressure if we assume fully mobilization of passive pressure and neglect the friction under the foundation.

As per the above figure, soil cover above the base is 0.5 m and thickness of the base is 0.5m.

Depth of the shear key           = 1.6 - 0.5 - 0.5
                                               = 0.6 m 

Provide a shear key of height 600mm.

It also note that we need to check the pressure under the foundation and it should be bellow the allowable bearing capacity of the soil. Further you may refer other design form list of designs on your left or click hear for beam design.