## 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.

Comprehensive shallow foundation design. A square spread footing is to be designed to support a column. The load on the column, including the column weight, is 800 kN. The foundation rests in homogeneous sandy clay. Geotechnical investigation found the soil’s strength parameters are c′ = 38 kN∕m² and ′ = 25∘. The groundwater table is at the ground surface. The saturated unit weight is 19 kN∕m³. The soil’s Poisson’s ratio is 0.5. The soil’s elastic modulus increases linearly with depth: Es = 4, 000(kN∕m²) + 230(kN∕m²∕m) × z, and z starts from the bottom of the foundation. The thickness of the foundation slab is chosen to be 0.5m, the elastic modulus of the foundation is 1.2 × 107kN∕m².The initial void ratio, compression index, swell index, and preconsolidation pressure are assumed to be consistent throughout the depth. Their values are e0 = 0.45, cc = 0.33, cs = 0.05, c′ = 100 kN∕m². Geotechnical investigation also found the homogeneous sandy clay extends to significant depth. Design the shallow foundation by performing the following tasks:

(1) Determine the foundation embedment depth. Use the general bearing capacity theory to determine foundation dimensions to satisfy a minimum factor of safety of 3.0.

(2) Calculate the allowable bearing capacity based on the actual dimensions of the foundation that are generally accepted in field construction.

(3) 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.

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

(5) Determine primary consolidation settlement of the saturated clay layer until the depth where vertical stress increase is 10% of the in situ effective stress. When calculating the settlement, 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 be calculated. If any parameter is needed but not provided in the problem statement, make appropriate assumptions and explicitly state them.

### Explain why attenuation is not a big problem in PET.

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Suppose a PET detector comprises four square PMTs (arranged as a 2 by 2 matrix) and a single BGO crystal with slits made in such a way that it is….