3.1 For a given soil, show that 1 + sat Ysat = n Yw W sat 3.2 For a given soil, show that Ysat Yd Ya - Ysat + Yw 3.3 For a given soil, show that nyw W. sat Y sat nyw The moist weight of 2.83 X 10-3 m³ of soil is 55.5 x 10-3 kN/m³. If the moisture content is 14% and the specific gravity of soil solids is 2.71, determine the following: a. Moist unit weight b. Dry unit weight c. Void ratio

Refer to the soil in Problem 4.5. Using the Casagrande plasticity chart, graphically estimate the shrinkage limit of the soil as shown in Figure 4.22. 4.5 The following data were obtained by conducting liquid limit and plastic limit tests on a soil collected from the site. Liquid limit tests: Plastic limit test: PL = 19.3% a. Draw the flow curve and determine the liquid limit. b. Using the Casagrande plasticity chart (Figure 4.21), determine the soil type.

The properties of seven different clayey soils are shown below (Skempton and Northey, 1952). Investigate the relationship between the strength and plasticity characteristics by performing the following tasks: a. Estimate the plasticity index for each soil using Skemptons definition of activity [Eq. (4.28)]. b. Estimate the probable mineral composition of the clay soils based on PI and A (use Table 4.3) c. Sensitivity (St) refers to the loss of strength when the soil is remolded or disturbed. It is defined as the ratio of the undisturbed strength (f-undisturbed) to the remolded strength (f-remolded)) at the same moisture content [Eq. (12.49)]. From the given data, estimate f-remolded for the clay soils. d. Plot the variations of undisturbed and remolded shear strengths with the activity, A, and explain the observed behavior.

Results from a liquid limit test conducted on a soil are given below. a. Determine the liquid limit of the soil. b. If it is known that the PI = 6.5, what would be the plastic limit of the soil? c. Determine the liquidity index of the soil if win situ = 23.8%