3D Soil-Structure Interaction Analysis of Cantilever Retaining Walls

Retaining walls are structures used to retain earth fill, and have found wide applications in buildings and highway construction. Traditionally, cantilever retaining walls are designed as line elements where the width of the cantilever is analysed per unit strip (usually per metre length). The base of the cantilever is usually considered as rigid, and a result, a linear pressure distribution under the base is usually assumed. In this post, we are going to show that cantilever retaining walls can interact with the soil supporting them to affect the settlement, internal forces, and base pressure distribution.


The factors usually checked out for in design of cantilever retaining walls are;

(1) Overturning
(2) Sliding
(3) Bearing capacity
(4) Uplift (rarely critical)
(5) Structural resistance

Methodology
We are going to consider the analysis and design of the retaining wall with the dimensions and soil properties shown in Figure 1.

Fig 1: Cantilever retaining wall on sand

The retaining wall was modelled using plate elements of size 0.5m x 0.5m on Staad Pro software with a unit weight of 24 kN/m3, while the soil was modelled using 8-noded solid element with the elastic properties indicated in Figure 1. Each soil element was modelled as a cuboid with a length and width of 0.5m, and thickness (depth) of 1m. The solids were stacked on each other to achieve the formation thickness of 7m. The rock layer was achieved by supporting the last nodes of the soil elements using pinned support. The width of the retaining wall was taken as 3m. 

For ultimate limit state, the permanent actions (self weight of concrete and earth fill) were factored with a partial factor of 1.35, while the variable action (surcharge) was multiplied by a partial factor of 1.5. The effect of ground water was not considered in the analysis. The 3D rendering of the soil and retaining wall is shown in Figure 2.

Fig 2: 3D Soil-Retaining Wall Modelling on Staad Pro.

Results
(1) Settlement
The settlement profile and deflection of the retaining wall at serviceability limit state is shown in Figure 3.

Fig 3: Deflection and Settlement Profile of the soil

Maximum settlement at the toe SLS = 19.647 mm
Settlement at the heel (SLS) = 14.856 mm
Deflection of the cantilever = 35.493 mm


(2) Pressure distribution
The pressure distribution under the retaining wall at serviceability and ultimate limit states are shown in Figures 4 and 5 respectively. As expected, the maximum pressure occurred at the toe, while minimum pressure occurred at the heel. The pressure distribution was observed to be non-linear, but a little consideration will show that linear approximation can be adopted for design purposes. At SLS, a minimum pressure of 52.6 kPa at the heel, and a maximum pressure of 184 kPa was found to be concentrated at the corners of the toe.

Fig. 4: Base pressure distribution (SLS)
Fig. 5: Base pressure distribution (ULS)

(3) Bending moment
The bending moment on the walls at ULS are shown in Figures 6 and 7.

Fig. 6: Vertical bending moment on the retaining wall
Fig 7: Horizontal bending moment on the retaining wall

(4) Stability Analysis (SLS)

(a) Sliding
Summation of horizontal forces = 401.99 kN
Summation of vertical forces = 1876.8 kN

Let the coefficient of friction of the base against sliding be tan(2/3 x 30o) = 0.363

Factor of safety against sliding = [1876.8 x 0.363] / 401.99 = 1.69 (Okay)

(b) Overturning
Overturning moment = 2612.6 kNm
Stabilising moment = 12356.42 kNm

Factor of safety against overturning = 12356.42/2612.6 = 4.729 (Okay)

The design for the reinforcements can be done accordingly. Kindly carry out manual analysis of the same retaining wall and forward it to ubani@structville.com for consideration.

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