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How is Mat Foundation Idealized in Software “SAFE”? Part-1

In previous post we have discussed many aspects of raft foundation including different parameters used in mat foundation design. We have already discussed about modulus of subgrade reaction, assumptions and considerations to analyze mat as rigid or flexible foundation, loads that should account in mat foundation design, thickness rigidity relationship of mat, and thickness deflection relationship of mat. In this post we will learn about analysis model that are used in computer software SAFE. We will discuss the foundation idealization in two posts as part-1 and part-2. Please stay tuned with this blog.

In this model finite elements are formed from object based model. Rectangular finite element mesh is developed depending on maximum allowable element size.

Structural idealization of supporting soil and raft in SAFE

Computer oriented method for structural analysis is used to solve plates(raft) supported on elastic foundation. These rectangular finite elements are interconnected to adjacent one only at corners (nodes) and a isolated spring that resembles to soil are used in modeling.

Raft foundation is analyzed in SAFE based on classical theory for thick plates supported on the winkler foundations. The isolated spring assumed in modeling soil is called winkler foundation. This theory takes in to account the deformation due to transverse shear of the plate. This model is shown in the figure below.

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How is Mat Foundation Idealized in Software “SAFE”? Part-2

In the previous post we have discussed about modeling procedure of mat foundation in computer software SAFE. The rest of the discussion will be discussed in this post. We were on classical theory for thick plates supported on winkler foundation. We have already known that this method take into account deformations due to transverse shear of the plate.

Formulation is derived from assumptions that:

Assumptions for formulation of classical theory for thick plates supported on winkler foundation

The formulation for finite element-isoparameric, four noded, rectangular elements have freedom of three degree per node, is assumed. The three degree freedoms include:

Degree of freedom of finite element mash per node for raft foundation analysis with SAFE

1. Transverse displacement=w

2. Rotation around X-axis=θx

3. Rotation around X-axis= θy

Shape functions of independent bilinear properties are taken account for rotational and displacement degree of freedom. There force deflection equation can be derived for plate foundation element, by equating the first variation for total strain energy to zero for the required plate foundation system.

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Revolution of Mat Foundation Analysis with the Development of Electronic Foundation Solution

Flexural rigidity of mat and soil modulus of subgrade reactions are not common term to foundation engineers who are analyzing and designing a mat foundation with the rigid beam method as discussed in earlier posts. They are used to assume the infinite rigidity of mat foundation and above two terms are totally ignored. This assumption leads to a unrealistic modeling of mat foundation as discussed before.

Conventional methods were/are used as they are simple and complexity in elastic analysis like finite element method cannot be solved easily as computing device are not available to foundation engineers. Now-a-days due to revolution of electronic calculation method using computer programming numerous types of input of parameters and their resulting solution can be predicted within minutes(like solution of any degree of matrix can be solved within few seconds). The advanced silicon chip technology provides computer extensive capability to solve laborious calculations and new advancement of these technology make such devices cheaper than ever.

Finite element analysis with SAFE-09: Deflected shape of mat due to earthquake loading

Thus chances of errors and limitation of input many parameters are removed and solution like finite element method can solved easily.

We emphasize on the finite element method as it is the finest way to analyze mat foundation. In this method soil beneath mat is considered as elastic continuum and the mat itself as a plate. The finite element method of mat analysis can be solved conveniently with software “SAFE”. Friends keep an eye on the next posts to have an idea about SAFE to solve mat.

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What is Parametric Study in Mat Foundation Analysis?

In the last posts about mat foundation, we have discussed many parameters that are used in analysis and design of mat foundation. Say these parameters are:

a. Es=modulus of elasticity of soil

b. µ =Poisson’s ratio

c. Ks=q/ δ=Modulus of subgrade reaction in vertical direction

Many parameters with this parameters cannot be predicted accurately as their have many difficulties. To account this problem, geotechnical engineers and structural engineers together perform a study called parametric study.

In this parametric study engineers vary the values that are used in foundation design. There have a range of variation. This is Finite element analysis with SAFE-09: Deflected shape of mat due to earthquake loading(1/2 X furnished value) to (10Xfurnished value)

With this wide range of variations in parameters, the geotechnical engineers carefully review the results through the whole design process.

When engineers are not satisfied with solutions, then it is assumed appropriate adjustments are done in development concept. Now we will know what the adjustments are. The adjustments are:

1. Reduction in weight of structure

2. Enlarging mat foundation area

3. Reducing net pressure changing mat base area

It should keep in mind that, the adjustments should take in presence of both structural and geotechnical engineers.