Analysis of Anchored Wall Simply Supported at Heel
Anchored wall simply supported at the heel is analyzed as a continuous beam using the deformation variant of the finite element method in order to comply with the assumption of a simply supported structure at the heel. The actual analysis is preceded by the determination of load due to earth pressure applied to the structure. The pressure acting on the back of a structure is assumed as active pressure, while the front face is loaded by passive pressure.
The passive pressure can be reduced with the help of the coefficient of reduction of passive pressure. Assuming the actual magnitude of the passive earth pressure provides deformations of the analyzed structure, which cannot usually occur. The actual passive pressure can attain for walls free of deformation the value of pressure at rest as well as all intermediate values up to the value of passive pressure for a fully deformed wall (rotation app. 10 mRad - i.e. deformation 10 mm per 1 m of structure height). Therefore it is reasonable to consider reduced values of the passive earth pressure setting the value of the "Coefficient of reduction of passive pressure" to less than or equal to one. The following values are recommended:
- 0.67 reduces deformations app. by one half
- 0.33 deformations attain approximately twenty percent of their original values
The program offers two options to determine active pressure:
- calculation from input soil parameters, water, surcharge, terrain including the introduction of the minimum dimensioning pressure
- inputting an arbitrary distribution of earth pressure up to the depth of zero point (this way it is possible to introduce an arbitrary redistribution of earth pressure).
Zero-value point, i.e. the point at which the overall pressure equals zero is determined by the following expression:
where: | u | - | depth of the zero-value point |
σa | - | magnitude of the active pressure behind the structure at the ditch bottom | |
K | - | coefficient of the overall pressure | |
γ | - | unit weight of the soil below the ditch bottom |
For simply supported structures it is assumed that the moment and shear force are zero at the heel. The program first places the end of a structure into the zero-value point, and then it looks for the end beam location x, where the above condition is fulfilled (see Fig.). The solution procedure for a multiplied anchored walls is identical.
Analysis of anchored wall simply supported at heel