## Calculate the factor of safety for bearing capacity.

Comprehensive mat foundation design. A mat foundation is to be designed. The dimensions of the mat are 30 m by 30 m. The stress caused by the superstructure and the mat at the bottom of the foundation is 480 kN∕m². The embedment depth of the mat foundation is determined to be 10 m below the ground surface, and the thickness of the mat is 3.0 m. The groundwater table (GWT) is at the bottom of the foundation. The subsoil is homogeneous clayey soil with the following parameters.

Soil strength parameters: c′ = 75 kN∕m², ′ = 25∘.

Above GWT ∶ = 17.5 kN∕m³; below GWT ∶ sat = 18.5 kN∕m³.

Poisson’s ratio μ = 0.4.

The soil’s elastic modulus increases linearly with depth: Es(kN∕m²) = 15, 000 (kN∕m²) + 750 (kN∕m²/m) × z and z starts from the bottom of the foundation.

The elastic modulus of the foundation is Ef = 1.25 × 107kN∕m².

Compressibility parameters: e0 = 0.55, cc = 0.3, cs = 0.06, ′c = 100 kN∕m².

Geotechnical investigation also found the homogeneous sandy clay extends to significant depth. Design the mat foundation by performing the following tasks:

(1) Calculate the factor of safety for bearing capacity.

(2) Determine the depth at which the vertical stress increase is 10% of the in situ effective stress. Any method can be used to calculate the vertical stress increase.

(3) Determine the elastic settlement of the soil layer until the depth where the vertical stress increase is 10% of the in situ effective stress. Use the Mayne and Poulos method.

(4) Determine primary consolidation settlement of the saturated clay layer until the depth where the vertical stress increase is 10% of the in situ effective stress. To do so, first divide the soil layer into sublayers based on Figure 3.24; then calculate the average vertical stress increase in each of the sublayers; then primary consolidation settlement of each layer can then be calculated. If any parameter is needed but not provided in the problem statement, make appropriate assumptions and explicitly state them.

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