Chapter 4, Problem 4.1CTP

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 Skempton’s 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 (S_t) refers to the loss of strength when the soil is remolded or disturbed. It is defined as the ratio of the undisturbed strength (τ_{f-undisturbed}) to the remolded strength (τ_f-remolded)) at the same moisture content [Eq. (12.49)]. From the given data, estimate τ_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.

To determine

Find the plasticity index for each soil using Skempton’s definition of activity.

Explanation of Solution

Determine the plasticity index of the Beauharnais soil using the relation.

$A=\frac{PI}{\text{\%}\text{of}\text{clay-size}\text{fraction, by}\text{weight}}$

Here, A is an activity.

Substitute 0.52 for A and 79 for % of clay–size fraction, by weight.

$\begin{array}{l}0.52=\frac{PI}{79}\\ 0.52\times 79=PI\\ PI=41.08\end{array}$

Similarly, calculate the plasticity index for the remaining soils.

Determine the remolded shear strength of the Beauharnais soil using the relation.

${\tau }_{f-\text{remolded}}=\frac{{\tau }_{f-\text{undisturbed}}}{S_t}$

Here, ${\tau }_{f-\text{undisturbed}}$ is the undisturbed shear strength and $S_t$ is the sensitivity.

Substitute $18{\text{kN/m}}^{\text{2}}$ for ${\tau }_{f-\text{undisturbed}}$ and 14 for $S_t$.

$\begin{array}{c}{\tau }_{f-\text{remolded}}=\frac{18}{14}\\ =1.3{\text{kN/m}}^{\text{2}}\end{array}$

Similarly, calculate the remolded shear strength of the remaining soils.

Summarize the calculated values of plasticity index and the remolded shear strength as in Table 1.

Soil	% Clay fraction $\left(<2\text{μm}\right)$	Activity A	Plasticity Index
Beauharnois	79	0.52	41.08
Detroit I	36	0.36	12.96
Horten	40	0.42	16.80
Gosport	55	0.89	48.95
Mexico City	90	4.5	405
Shell haven	41	1.33	54.53
St.Thuribe	36	0.33	11.88

To determine

Find the probable mineral composition of the clay soils based on PI and A.

Explanation of Solution

Determine the probable mineral composition of the clay soils based on PI and A.

Refer Table 4.3, “Typical values of liquid limit, plastic limit, and activity of some clay minerals” in the textbook.

Take the mineral composition of the Beauharnois soil as Illite for the activity value of 0.52 and the plasticity index value of 41.08.

Therefore, the mineral composition of Beauharnois soil is Illite.

Similarly, calculate the probable mineral composition of the remaining soils.

Summarize the calculated values of mineral composition as in Table (2).

Soil	Activity A	Plasticity Index	Mineral composition
Beauharnois	0.52	41.08	Illite
Detroit I	0.36	12.96	Kaolinite
Horten	0.42	16.80	Kaolinite
Gosport	0.89	48.95	Illite
Mexico City	4.5	405	Montmorillonite
Shell haven	1.33	54.53	Montmorillonite
St.Thuribe	0.33	11.88	Kaolinite

To determine

Find the remoulded shear strength of the clay soil.

Explanation of Solution

Determine the remoulded shear strength of the Beauharnais soil using the relation.

${\tau }_{f-\text{remolded}}=\frac{{\tau }_{f-\text{undisturbed}}}{S_t}$

Here, ${\tau }_{f-\text{undisturbed}}$ is the undisturbed shear strength and $S_t$ is the sensitivity.

Substitute $18{\text{kN/m}}^{\text{2}}$ for ${\tau }_{f-\text{undisturbed}}$ and 14 for $S_t$.

$\begin{array}{c}{\tau }_{f-\text{remolded}}=\frac{18}{14}\\ =1.3{\text{kN/m}}^{\text{2}}\end{array}$

Similarly, calculate the remolded shear strength of the remaining soils.

Summarize the calculated values of remolded shear strength as in Table 3.

Soil	Activity A	Undisturbed Shear strength $\left({\tau }_{f-\text{undisturbed}}\right)$$\left({\text{kN/m}}^{\text{2}}\right)$	Sensitivity $\left(S_t\right)$	Remoulded Shear strength $\left({\tau }_{f-\text{remolded}}\right)$$\left({\text{kN/m}}^{\text{2}}\right)$
Beauharnois	0.52	18	14	1.3
Detroit I	0.36	17	2.5	6.8
Horten	0.42	41	17	2.4
Gosport	0.89	29	2.2	13.2
Mexico City	4.5	46	5.3	8.7
Shell haven	1.33	36	7.6	4.7
St.Thuribe	0.33	38	150	0.3

To determine

Plot the variations of undisturbed and remolded shear strengths with the activity A.

Explanation of Solution

Refer Table 3.

Plot the graph between the undisturbed, remolded shear strengths with the activity A as in Figure 1.

The shear strength of the clay obtains from two components, one is cohesion, which is the cementing force between particles, and second one is frictional resistance, which is mainly due to the particle movement of one particle over another. The cohesion contribution is greater to the shear strength, when the clay activity is greater. Although no reliable correlation can be developed from Figure 1, both the undisturbed and remolded shear strengths certainly show increasing trends as the activity increases.