1.2 Soil Consolidation and Settlement

Overview of Settlement

Settlement is the vertical downward movement of the ground surface caused by applied loads, such as foundations, embankments, or structural fill. For the PE Construction exam, understanding how different soil types respond to loading is critical for anticipating foundation performance and planning construction sequencing. Total settlement consists of three components: immediate (elastic) settlement, primary consolidation settlement, and secondary compression (creep).

Immediate (Elastic) Settlement

Immediate settlement occurs rapidly upon application of the load, without a change in the moisture content of the soil. It is governed by the elastic properties of the soil (Young's modulus, $E$, and Poisson's ratio, $\nu$). Immediate settlement is the predominant form of settlement in coarse-grained, cohesionless soils like sands and gravels. Because water drains quickly from these soils, the settlement occurs almost synchronously with the construction process. It is typically calculated using elastic theory equations provided in the reference handbook.

Primary Consolidation Settlement

Primary consolidation is a time-dependent process that occurs exclusively in saturated, fine-grained soils like clays and silts. When a load is applied to a saturated clay, the low permeability of the soil prevents water from draining quickly. Initially, the applied load is carried entirely by an increase in pore water pressure (excess pore pressure). Over time, as water slowly squeezes out of the soil voids, the excess pore pressure dissipates, and the load is transferred to the soil skeleton (effective stress increases). This decrease in void volume causes primary consolidation settlement.

The magnitude of primary consolidation settlement ($S_c$) for a normally consolidated clay layer of thickness $H_c$ is calculated using the compression index ($C_c$):

$S_c = \frac{C_c H_c}{1 + e_0} \log\left(\frac{\sigma_{v0}' + \Delta\sigma'}{\sigma_{v0}'}\right)$

where:

• $C_c$ = Compression index
• $H_c$ = Thickness of the compressible clay layer
• $e_0$ = Initial void ratio
• $\sigma_{v0}'$ = Initial vertical effective stress at the midpoint of the clay layer
• $\Delta\sigma'$ = Increase in vertical effective stress due to the applied load

If the clay is overconsolidated (i.e., it has experienced a higher stress in the past than its current state), the recompression index ($C_r$) is used instead of $C_c$ for stresses up to the preconsolidation pressure. $C_r$ is typically 1/5 to 1/10 the value of $C_c$, meaning overconsolidated clays settle much less than normally consolidated clays.

Time Rate of Consolidation

Because clay has low permeability, primary consolidation can take months or years. The rate at which consolidation occurs is governed by the coefficient of consolidation ($c_v$), which incorporates both the permeability and the compressibility of the soil. The time ($t$) required to reach a certain degree of consolidation ($U$) is related to the time factor ($T_v$) and the longest drainage path ($H_{dr}$):

$t = \frac{T_v H_{dr}^2}{c_v}$

The drainage path $H_{dr}$ is crucial:

• For a clay layer draining in one direction (e.g., bounded by rock on the bottom and sand on top), $H_{dr}$ equals the full thickness of the clay layer.
• For a clay layer draining in two directions (e.g., bounded by sand on both top and bottom), $H_{dr}$ equals half the thickness of the clay layer.

Secondary Consolidation (Creep)

Secondary consolidation occurs after the excess pore water pressure has fully dissipated (i.e., after primary consolidation is complete). It is a slow, ongoing plastic deformation of the soil skeleton under constant effective stress. Secondary settlement is most significant in highly organic soils and soft clays, and is calculated using the secondary compression index ($C_\alpha$).

Surcharge Preloading Logic

In construction, if a site contains soft clay that will settle unacceptably under a new building, a technique called surcharge preloading is often used. A temporary mound of earth (surcharge) is placed over the site before construction. The weight of the surcharge induces primary consolidation. Once the required settlement is achieved, the surcharge is removed, and the building is constructed on the now "overconsolidated" clay, which will experience very little future settlement. Wick drains (prefabricated vertical drains) are often installed to shorten the drainage path ($H_{dr}$), significantly accelerating the consolidation process.

Worked Example: Calculating Primary Consolidation Settlement

Problem: A 10-ft thick layer of normally consolidated clay has an initial void ratio of 1.20 and a compression index ($C_c$) of 0.45. The initial vertical effective stress at the midpoint of the clay layer is 1,500 psf. A newly constructed embankment will add a vertical stress increase of 800 psf at the midpoint of the clay layer. Calculate the expected primary consolidation settlement in inches.

Solution:

1. Identify the given parameters:

   • $H_c = 10 \text{ ft} = 120 \text{ inches}$
   • $e_0 = 1.20$
   • $C_c = 0.45$
   • $\sigma_{v0}' = 1500 \text{ psf}$
   • $\Delta\sigma' = 800 \text{ psf}$

2. Apply the primary consolidation settlement formula: $S_c = \frac{C_c H_c}{1 + e_0} \log\left(\frac{\sigma_{v0}' + \Delta\sigma'}{\sigma_{v0}'}\right)$

3. Substitute the values: $S_c = \frac{0.45 \times 120}{1 + 1.20} \log\left(\frac{1500 + 800}{1500}\right)$

4. Calculate the leading term: $\frac{54}{2.20} \approx 24.545$

5. Calculate the logarithm term: $\log\left(\frac{2300}{1500}\right) = \log_{10}(1.533) \approx 0.1856$

6. Calculate the final settlement: $S_c = 24.545 \times 0.1856 \approx 4.56 \text{ inches}$

Answer: The expected primary consolidation settlement is approximately 4.56 inches.

Exam Tips

• Pay close attention to units, particularly ensuring that the layer thickness $H_c$ is converted to inches if the final answer requests inches.
• Remember that elastic settlement applies primarily to granular soils and happens immediately, while consolidation settlement applies to cohesive soils and happens over time.
• For drainage paths, always check the soil stratigraphy. A two-way drainage condition cuts the drainage path in half, which reduces the time to achieve a specific degree of consolidation by a factor of four ($t \propto H_{dr}^2$).