Seismic Design of Mat
· NEHRP Seismic Design Technical Brief No. 7
· Seismic Design of Reinforced Concrete Mat Foundations. A Guide for Practicing Engineers
· By Ron Klemencic, Ian S. McFarlane, Neil M. Hawkins, Sissy Nikolaou
· NEHRP (National Earthquake Hazards Reduction Program) Technical Briefs are published by NIST, the National Institute of Standards and Technology, as aids to the efficient transfer of NEHRP and other research into practice, thereby helping to reduce the nation’s losses from earthquakes.
· Seismic design of reinforced concrete mat foundations has advanced significantly in the last twenty years.
· As analytical capabilities have improved, primarily in the form of finite element analysis, the mathematical modeling of these continuous structural elements has led to seemingly more precise designs.
· Yet, fundamental questions still remain regarding the seismic performance of these thick foundation systems.
Following Aspects Must be Considered during Mat Design
2. Soft soil and site amplification
3. FoS against overturning and sliding
4. Drift due to soil deformation during EQ and wind
5. Rebar detailing
6. Punching shear reinforcement
Basic Foundation Design Procedures
1. ACI 318 (ACI-ASCE Committee 326)
· Foundations are designed using allowable stress for the soil and strength design (USD) for the concrete foundation
· Bearing failure of the soil under the foundation
· serviceability failure because of excessive differential settlements causing nonstructural or structural damage to the superstructure
· Excessive total settlements
3. Limiting conditions
· local flexural failure of the foundation (including reinforcement anchorage failure)
4. shear failure of the foundation
· Soil pressures were traditionally calculated by assuming linear elastic action of the soil in compression and no tension capacity offered by the soil.
5. The stress under the foundation is given by:
q = P/A ± My/I
where, as illustrated in Figure 2-1(a) and Figure 2-1(b):
P = axial force
A = area of contact surface between the soil and the foundation
I = moment of inertia of contact area A
M = moment about centroidal axis of area A
y = distance from centroidal axis to position
where q is calculated
6. If separation (uplift) between the soil and the foundation is to be avoided, the eccentricity e = M/P must lie within the kern of the contact surface.
The kern area, which is shaded area in Figure 2-1(c), is the area for which applied loads within that region will produce only compression over the area of the footing.
· American Concrete Institute 1988
The suggested design procedure using strength methods for proportioning the mat was as follows:
1. Proportion the mat plan using unfactored loads and overturning moments as:
The value q is then scaled to a pseudo “ultimate” value as:
2. Compute the minimum required mat thickness based on punching shear at critical columns and walls without the use of shear reinforcement
3. Design the reinforcing steel for bending based on the strip methods described in the ACI 336.2R-66 report.
4. Run a computer analysis of the resultant mat, such as with the finite element method as described in the ACI 336.2-88 report. Revise the rigid body design as necessary.
Punching Shear Strength of Mat
Two-Way Shear (Punching Shear)
Punching shear tests of slabs have shown that Equation 11-33 of ACI 318, Vc = 4√( f ’c)bod can be unconservative for thick members with low reinforcement ratios (Guandalini et al. 2009). *****
In addition, ACI 318 §188.8.131.52 requires that Vc ≤ 2√( f ’c)bod when reinforcement is provided for punching shear resistance. *****
Therefore, a value of Vc = 2√( f’c)bod is recommended for design purposes
Beam Shear Strength of Mat
One-Way Shear (Beam Shear)
Peak shear stresses have traditionally been considered as 2√f ’c , while some research (Reineck et al., 2003) suggests that for thick structural elements in one-way shear this is unconservative, and √f’c is a more appropriate shear stress threshold when no vertical reinforcement is provided
One-Way Shear and Vertical Reinforcement
When vertical reinforcement in accordance with ACI 318 §11.4.6 is provided in a mat foundation, aggregate interlock is maintained, and it is recommended to use Vc = 2√f ’c bod in combination with Vs corresponding to the vertical reinforcement provided. Therefore, a thinner mat may be possible by providing a nominal amount of vertical reinforcement as compared to a mat without vertical reinforcement
ACI 318 – 08 >>> 11.4.6 — Minimum shear reinforcement
184.108.40.206 — A minimum area of shear reinforcement, Av,min, shall be provided in all reinforced concrete flexural members (prestressed and nonprestressed) where Vu exceeds 0.5φVc, except in members satisfying one or more of (a) through (f):
(a) Footings and solid slabs; (b) ……….
Reason of Conservative Design of Mat
1. There is great difficulty in predicting subgrade responses and in assigning even approximate properties to the soils
2. Because of soil-strata thickness, variations in soil properties both horizontally and vertically, and rate of loading.
3. There are effects of mat shape and variation in superstructure loads and their development, and there are effects of superstructure stiffness on mat response and vice versa.
4. For those reasons, mats were conservatively designed to ensure adequate performance.
Now a days, analysis of a mat foundation is typically performed using finite element analysis software
· soil spring properties
2. Analysis results
· bearing pressure distributions
· mat deformations
· moment and shear diagrams
· Details flexural reinforcement
Typical Modeling Practice
1. Finite element analysis of mat foundations typically assumes gross section concrete stiffness with no cracking.
2. Developing a numerical model for a mat foundation analysis model, stiffness of the complete structure should be considered
3. For shear walls or basement walls above a mat foundation, the in-plane flexural stiffness should be added to the analysis model
4. This can be accomplished with a very deep beam or slab element
5. At elevator pits, the pit configuration should be reflected in the analysis model
6. Where the pit depth is less than the mat thickness, a reduced mat thickness should be used
7. For pits that extend below the mat foundation, a combination of reduced mat thickness and flexural releases should be used to reflect the pit configuration
8. Dishing (or cupping) can be visualized by considering the difference in pressure at the center of a uniformly loaded mat as compared to the very edge of the mat
9. The pressure at the edge of the mat dissipates quickly into the soil continuum because of lack of pressure on the adjacent soil, but the pressure at the center of the mat dissipates more slowly because of the adjacent loaded soil
10. To accurately model this effect, a variable subgrade modulus may need to be used in the analysis model
11. To select the appropriate modulus, iterations must be performed between the structural engineer and geotechnical engineer
12. Dishing (or cupping) can be visualized by considering the difference in pressure at the center of a uniformly loaded mat as compared to the very edge of the mat
13. The pressure at the edge of the mat dissipates quickly into the soil continuum because of lack of pressure on the adjacent soil, but the pressure at the center of the mat dissipates more slowly because of the adjacent loaded soil
14. To accurately model this effect, a variable subgrade modulus may need to be used in the analysis model
15. To select the appropriate modulus, iterations must be performed between the structural engineer and geotechnical engineer
16. Depending on the subgrade behavior, dishing may have a relatively small effect on soil pressure distribution but may have a more significant effect on bending moments in the mat foundation (Horvilleur and Patel 1995).