Question

1. Use Figure 1 and Table 1 for the following:
   1. Compute the vertical effective stress (σ'_v) in kN/m² at the center of the clay layer prior to the construction of the footing.
   2. Assuming a load of 1150 kN, use the Boussinesq procedure to determine increase in the vertical stress (Δσ) in kN/m² at the center of the clay layer below the center of the footing.
   3. Assuming the values that you computed in (a) and (b) are representative for the entire thickness of the clay layer, calculate the ultimate primary consolidation settlement (ΔH_final) in mm that will occur in the clay layer from placement of the footing. Use an empirical relation to estimate the compression index.
   4. A consolidation test was performed on a 25 mm thick, undisturbed sample taken from the center of the clay layer. The time and dial gauge readings obtained from an increase in pressure on the specimen from 200 to 400 kN/m² are given in Table 1. Use the "logarithm of time" method (i.e., Casagrande procedure) to determine the coefficient of consolidation (c_v) in mm²/min.
   5. Using Terzaghi's 1D consolidation theorem, calculate and plot the predicted settlement of the footing as a function of time (i.e., ΔH(t) vs. time), where ΔH(t) is in mm and time is in days. [Compute ΔH(t) at enough times so that you can reasonably construct the requested plot. Also, compute ΔH(t) for times long enough that ΔH_finalis reached.]
   6. Based on the inherent assumptions in Terzaghi's 1D consolidation theorem and those made above versus actual field conditions, would you expect the footing in Figure 1 to settle faster or slower than predicted in (e), why?

   7. Time (t) from the application of pressure increment (min)	Dial gauge reading (mm)
      0	4.995
      0.1	5.010
      0.25	5.033
      0.5	5.053
      1	5.107
      2	5.153
      4	5.211
      8	5.287
      15	5.351
      30	5.379
      60	5.400
      120	5.418
      290	5.434
      395	5.440
      1230	5.460

      Table 1. Time vs. deformation readings for a stress increase from 200 to 400 N/m².

Answer 1

Where,

T_v = Time factor for 50% consolidation

= 0.197 (standard value)

H = Thickness of the sample tested

= 25 mm (given)

t₅₀ = Time taken for 50% consolidation (will be obtained from graph.

From the above graph we got,

t₅₀ = 2.8 min.

Therefore using the above equation,

C_v = (0.197 * 25²) / 2.8

C_v = 43.97 mm²/min