Engineering and Construction

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      a. The modulus of subgrade reaction can be determined from a plate load test (para 4-6) using a 1- by
1- foot plate


The equation above is valid for clays and assumes no increase in the modulus with depth, which is incorrect,
and may give k1,  which is too large.
For footings or mats on sand:

For a rectangular footing or mat of dimensions of B x mB:

       (  15m5)(10-3)

with a limiting value of ksf = 0.667ksl


      b. ks may be computed as ks = 36qa. (kips per square foot) (10-4)  which has been found to give values about as reliable as any method.  This equation assumes qa (kips per square foot) for a settlement of about 1 inch with a safety factor,

F ≅ 3.  A typical range of values of ks is given in table 3-7.

Table 3- 7.  An Engineering Evaluation of Shales

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a. Control of groundwater.   Exclude groundwater from the excavation by means of cutoffs, and provide for temporary or permanent pressure relief and dewatering by deep wells or wellpoints as described in TM 5-818-5/AFM 88-5.  Specify piezometers to measure drawdown levels during construction.  Specify the pumping capacity to achieve required drawdown during various stages of construction, including removal of the temporary system at the completion of construction.  Consider effects of drawdown on adjoining structures.

b. Downdrag.   Placement of backfill against basement walls or deep raft foundations constructed in open excavations results in downdrag forces if weight of backfill is significant with respect to structural loading.

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a. Stability.   The bearing pressure on mat foundations should be selected to provide a factor of safety of at least 2.0 for dead load plus normal live load and 1.5 for dead load plus maximum live load.  By lowering the base elevation of the mat, the pressure that can be exerted safely by the building is correspondingly increased, and the net increase in loading is reduced.  The bearing pressure should be selected so that the settlement of the mat foundation will be within limits that the structure can safely tolerate as a flexible structure.  If settlements beneath the mat foundation are more than the rigidity of the structure will permit, a
redistribution of loads takes place that will change the pressure distribution beneath the structure, as subsequently described.  The bearing capacity of loose sands, saturated silts, and low-density loess can be
altered significantly as a result of saturation, vibrations, or shock.  Therefore, the allowable bearing pressure and settlement of these soils cannot be determined in the usual manner for the foundation soils may be subject to such effects.  Replace or stabilize such foundation soils, as discussed later, if these effects are anticipated.

b. Conventional analysis.   Where the differential settlement between columns will be small, design the mat as reinforced concrete flat slab assuming planar soil pressure distribution.  The method is generally applicable where columns are more or less equally spaced.  For analysis,  the mat is divided into mutually perpendicular strips.

c. Approximate plate analysis.   When the column loads differ appreciably or the columns are irregularly spaced, the conventional method of analysis becomes seriously in error.  For these cases,  use an analysis based on the theory for beams or plates on elastic foundations.  Determine the subgrade modulus by the use of plate load tests.  The method is suitable, particularly for mats on coarse-grained soils where rigidity increases with depth.

d. Analysis of mats on compressible soils.   If the mat is founded on compressible soils, determination of the distribution of the foundation pressures beneath the mat is complex.  The distribution of foundation
pressures varies with time and depends on the construction sequence and procedure,  elastic and plastic deformation properties of the foundation concrete, and time-settlement characteristics of foundation soils.  As a conservative approach, mats founded on compressible soils should be designed for two limiting conditions: assuming a uniform distribution of soil pressure, and assuming a pressure that varies linearly from a minimum of zero at the middle to twice the uniform pressure at the edge.  The mat should be designed structurally for whichever distribution leads to the more severe conditions.

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General.  
When required footings cover more than half the area beneath a structure, it is often desirable to enlarge and combine the footings to cover the entire area.  This type of foundation is called a raft or mat foundation and may be cheaper than individual footings because of reduced forming costs and simpler excavation procedures.  A mat foundation also may be used to resist hydrostatic pressures or to bridge over
small, soft spots in the soil, provided the mat is adequately reinforced.  Although mat foundations are more difficult and more costly to design than individual spread footings,  they can be used effectively.

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Figure 5.2 shows various types of mat foundations. Based on economic considerations, mat foundations are often constructed for the following reasons (NAVFAC DM-7.2, 1982):

1. Large individual footings. A mat foundation is often constructed when the sum of individual footing areas exceeds about one-half of the total foundation area.

2. Cavities or compressible lenses. A mat foundation can be used when the subsurface exploration indicates that there will be unequal settlement caused by small cavities or compressible lenses below the foundation. A mat foundation would tend to span over the small cavities or weak lenses and create a more uniform settlement condition.

3. Shallow settlements. A mat foundation can be recommended when shallow settlements predominate and the mat foundation would minimize differential settlements.

4. Unequal distribution of loads. For some structures, there can be a large difference in building loads acting on different areas of the foundation. Conventional spread footings could be subjected to excessive differential settlement, but a mat foundation would tend to distribute the unequal building loads and reduce the differential settlements.

5. Hydrostatic uplift. When the foundation will be subjected to hydrostatic uplift due to a high groundwater table, a mat foundation could be used to resist the uplift forces.