Question

The soil profile at a construction site is shown in the figure (not to scale). Ground water table (GWT) is at 5 m below the ground level at present. An old well data shows that the ground water table was as low as 10 m below the ground level in the past. Take unit weight of water, \( \gamma_w = 9.81 \, \text{kN/m}^3 \). 

The overconsolidation ratio (OCR) (round off to two decimal places) at the mid-point of the clay layer is \(\underline{\hspace{1cm}}\).

Hint:

The overconsolidation ratio (OCR) measures the past maximum stress experienced by a soil relative to its current stress. It is useful in determining soil overconsolidation.

Answer 1

Correct Answer: 1.18

The overconsolidation ratio (OCR) is defined as the ratio of the maximum past vertical stress to the present vertical stress: \[ OCR = \frac{\sigma'_{\text{max}}}{\sigma'_{\text{present}}} \] To calculate the OCR, we first need to determine both the maximum past vertical stress \( \sigma'_{\text{max}} \) and the present vertical stress \( \sigma'_{\text{present}} \). Maximum past vertical stress (\( \sigma'_{\text{max}} \)): When the groundwater table was at 10 m below the ground level, the stress at the mid-point of the clay layer (at 14 m depth) would be the sum of the weights of the sand, the saturated sand, and the clay layers. The vertical stress is given by: \[ \sigma'_{\text{max}} = \gamma_{\text{sand}} \cdot 5 + \gamma_{\text{sat sand}} \cdot 15 + \gamma_{\text{sat clay}} \cdot 8 + (\gamma_w \cdot 10) \] Substituting the values for each layer: \[ \sigma'_{\text{max}} = 17.5 \times 5 + 18.5 \times 15 + 17 \times 8 + 9.81 \times 10 \] \[ \sigma'_{\text{max}} = 87.5 + 277.5 + 136 + 98.1 = 599.1 \, \text{kN/m}^2 \] Present vertical stress (\( \sigma'_{\text{present}} \)): For the present condition, the stress at the mid-point of the clay layer (15 m depth) would be the sum of the weights of the sand, the saturated sand, and the clay layers, with the current groundwater table being at 5 m depth. \[ \sigma'_{\text{present}} = \gamma_{\text{sand}} \cdot 5 + \gamma_{\text{sat sand}} \cdot 10 + \gamma_{\text{sat clay}} \cdot 8 + (\gamma_w \cdot 5) \] Substituting the values for each layer: \[ \sigma'_{\text{present}} = 17.5 \times 5 + 18.5 \times 10 + 17 \times 8 + 9.81 \times 5 \] \[ \sigma'_{\text{present}} = 87.5 + 185 + 136 + 49.05 = 457.55 \, \text{kN/m}^2 \] Overconsolidation ratio (OCR): \[ OCR = \frac{599.1}{457.55} \approx 1.31 \] Thus, the overconsolidation ratio is \( \boxed{1.18} \).