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Slab-on-Ground, Winkler Model


Theoretical   Approach
A slab system can be supported by walls and columns, or it can be treated as a slab-on-ground (waffle slab or raft). When slab-on-ground option is selected, there is no need for any other support (wall or column). This option can be selected on [Mesh and Material] input panel. Also, the soil stiffness in the vertical direction should be entered. The soil stiffness is an equivalent to the modulus of elasticity for the soil. The results are not sensitive on the value of the soil stiffness.

If there is some tension in the soil (negative deflection) the program will give an error message. On the Soil Pressure result screen, the zones with tension in the soil will be indicated. If this happens the model should be modified, so the slab panels in these problem zones are not in contact with the ground.

The slabs can be partially supported by walls and columns, and partially on ground.  This is epically useful for structures on slopes.

Each slab panel can be selected to be in-contact or not-in-contact with the soil.  This option may be used for reactive clays when part of the raft is in-contact with soil and the rest is not-in-contact with soil.

In addition to the elastic springs, defining the soil reaction n the Winkler mode, some piles may be used.  The piles can be placed at any location in the slabs.  This option can be used to control extensive settlement by introducing piles at the locations where the larges deflections.

wafle.jpg (53067 bytes)

Application Notes
This is some additional explanation about usage of SLABS software to analyse raft slabs (slab-on-ground). SLABS software models the soil as a series of independent elastic spring. There is one spring at each corner of all finite element triangle. The stiffness of the elastic spring is derived from the Modulus of Elasticity of the soil. This parameter is entered in the Mesh and Material input panel. The stiffness of the spring is calculated assuming uniformly stressed 1m depth block of soil deposit. In order to consider the actual depth of the soil deposit, the actual Modulus of Elasticity should be modified.

soil00.gif (3740 bytes)

The calculation of corrected Modulus of Elasticity of the soul is based on equalling of the settlement (d) of the soil deposit, assuming the actual stress distribution in the soil (figure left), and the deflection of the uniformly stressed 1x1m block of soil with some equivalent finite depth De (figure right). Both models should provide identical settlements (d). The procedure for calculation of the Ec (corrected Modulus of Elasticity) follows below: 1. Estimate the average soil pressure (q) for the raft slabs you are analysing. 2. Select an appropriate Modulus of Elasticity (E) for the soil type:

soft normally-consolidated clays: 1,400 - 4,200 kPa

medium clays: 4,200 - 8,400 kPa

stiff clays: 8,400 - 20,000 kPa

lose normally-consolidated sands: 7,000 - 20,000 kPa

medium normally-consolidated sands: 20,000 - 40,000 kPa

dense normally-consolidated sands: 40,000 - 48,000 kPa

3. Calculate the soil settlement (d), considering the actual stress distribution in the soil and the depth of the deposit, by using the actual E and q, and some equivalent size rectangular shape load. 4. The corrected soil Modulus of Elasticity, which should be used in SLABS is calculated as:

Ec = q / d

q - kN/(m*m)

d - m

Ec - kN/(m*m)

Note that the right-hand-side of the above expression is multiplied by 1m to balance the units. Generally, the corrected Modulus of Elasticity (Ec) will be smaller then the actual Modulus of Elasticity (E). The calculation of the equivalent Modulus of Elasticity is performed automatically by the software, base on the mechanical properties of the layers entered by the user.

layers.jpg (22748 bytes)

Note, that there are many other factors which will contribute to the slab-on-ground analysis. This is only a simplified linear elastic approach, which should be used very carefully in combination with some other alternative method to confirm the results. Also, it is recommended to vary the Modulus of Elasticity within +/- 30%, or even 50%, in order to examine its influence on the results.

Application   Example
SLABS model: 42m long, slab-on-ground, loaded with eight cylindrical fuel tanks:

soil01.gif (18011 bytes)


Detail of the loading pattern:
soil02.gif (10142 bytes)


Deflection Contours:
soil03.gif (17360 bytes)


Bending Moment Contours:
soil04.gif (24979 bytes)


Bending Moment Distribution:
soil05.gif (20679 bytes)


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