Dar Magazine I7 Page 25

abraj kudai

Uniform k modulus vs. discrete area method:

What's the difference?

Uniform k modulus method: A commonly practiced method

The normal design of a mat foundation looks at the subgrade
response, which is commonly modelled according to the
modulus of subgrade reaction k. A unified value of subgrade
reaction may allow a mat design to be completed. However,
the use of a uniform coefficient of subgrade reaction to analyze
and design mat foundations is an oversimplification of the soil
response and can lead to wrong designs.

Discrete area method: A method that better accounts for
subgrade response

The discrete area method is described in the American Concrete
Institute's (ACI) Special Publication SP152. It allows the structural-
geotechnical team to properly consider the mat subgrade
response using subgrade reaction theory and the principles
of soil mechanics.

According to the ACI, the geotechnical and structural engineers
need to work together. Both specialists need to cooperate on mat
foundation design, from early planning through construction.

With the discrete area method, the geotechnical engineer
selects a subgrade model using the principles of soil mechanics.
Then, the values of the coefficients of subgrade reaction
are calculated based on applied contact pressures.

The magnitude of the modulus of subgrade reaction at different
locations in the mat is determined by an iterative analysis.
This analysis is conducted in four steps, as follows:

Step 1 |

The structural engineer conducts a finite element

computer analysis of the mat using the geotechnical engineer's
best estimate of the modulus of subgrade reaction k.
In the first analysis, a uniform value of k is used over
the entire mat footprint.

Step 2 |

Using pressure distributions from Step 1, the

geotechnical engineer calculates the soil settlement at each node.
A new modulus of subgrade reaction is computed at each node.

Step 3 |

Using the modulus of subgrade reaction computed for

each node in Step 2, the structural engineer conducts a new
analysis and a new pressure distribution is obtained.

Step 4 |

Using the pressure distributions from Step 3, the

geotechnical engineer computes new settlements at each node.
A new k value is calculated at each node.

The procedure is followed until convergence is achieved.
This happens when the displacements predicted by the structural
engineer's finite element analysis match the settlements
predicted by the geotechnical engineer. Around two repetitions
of the procedure are normally required for convergence to occur.

Figure 7

Figure 6